Goldberger-treiman relation in the renormalized sigma model
Strubbe, H.J.
1972-01-01
The regularization and renormalization of the full sigma model is worked out explicitly in the tree and one-loop approximation. Various renormalized quantities relevant for chiral symmetry breaking are listed. The numerically calculated Goldberger-Treiman relation is also compared with experiment.
A Comment on the Renormalization of the Nonlinear Sigma Model
Bettinelli, D; Quadri, A; Bettinelli, Daniele; Ferrari, Ruggero; Quadri, Andrea
2007-01-01
We consider the recently proposed renormalization procedure for the nonlinear sigma model, consisting in the recursive subtraction of the divergences in a symmetric fashion. We compare this subtraction with the conventional procedure in power counting renormalizable (PCR) theories. We argue that symmetric subtraction in the nonlinear sigma model does not follow the lore by which nonrenormalizable theories require an infinite number of parameter fixings. Our conclusion is that only two parameters can be consistently used as physical constants.
On renormalization of Poisson-Lie T-plural sigma models
Hlavaty, Ladislav; Snobl, Libor
2013-01-01
Covariance of the one-loop renormalization group equations with respect to Poisson-Lie T-plurality of sigma models is discussed. The role of ambiguities in renormalization group equations of Poisson-Lie sigma models with truncated matrices of parameters is investigated.
Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model
Heller, Urs M.
1988-01-01
An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.
Monte Carlo renormalization-group investigation of the two-dimensional O(4) sigma model
Heller, Urs M.
1988-01-01
An improved Monte Carlo renormalization-group method is used to determine the beta function of the two-dimensional O(4) sigma model. While for (inverse) couplings beta = greater than about 2.2 agreement is obtained with asymptotic scaling according to asymptotic freedom, deviations from it are obtained at smaller couplings. They are, however, consistent with the behavior of the correlation length, indicating 'scaling' according to the full beta function. These results contradict recent claims that the model has a critical point at finite coupling.
Endowing the Nonlinear Sigma Model with a Flat Connection Structure: a Way to Renormalization
Ferrari, R
2005-01-01
We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term a` la Stueckelberg. However the paper is limited to the case where only the flat connection is present (no field strength term). The perturbative solution is constructed by using only the functional equations and by expanding in the number of loops. In particular we do not use a perturbative approach based on the path integral or on a canonical quantization. It is shown that there is no solution with trivial S-matrix. Then the model is embedded in a nonlinear sigma model. The solution is constructed by exploiting a natural hierarchy in the functional equations given by the number of flat connection insertions in the process. The amplitudes with the sigma field are simply derived from those of the flat connection. Unitarity is enforced by hand by using Feynman rules. We demonstrate the remarkable fact that in generic dimensions the naive Feynman rules yield amplitudes that satisfy the fu...
The sausage sigma model revisited
Suneeta, Vardarajan
2015-06-01
Fateev’s sausage sigma models in two and three dimensions are known to be integrable. We study their stability under renormalization group (RG) flow in the target space by using results from the mathematics of Ricci flow. We show that the three-dimensional sausage is unstable, whereas the two-dimensional sausage appears to be stable at least at leading order as it approaches the sphere. We speculate that the stability results obtained are linked to the classification of ancient solutions to Ricci flow (i.e., sigma models that are nonperturbative in the infrared regime) in two and three dimensions. We also describe a class of perturbations of the three-dimensional sausage (with the same continuous symmetries) which remarkably decouple. This indicates that there could be a new solution to RG flow, which is described at least perturbatively as a deformation of the sausage.
Generalized Poisson sigma models
Batalin, I; Batalin, Igor; Marnelius, Robert
2001-01-01
A general master action in terms of superfields is given which generates generalized Poisson sigma models by means of a natural ghost number prescription. The simplest representation is the sigma model considered by Cattaneo and Felder. For Dirac brackets considerably more general models are generated.
MCRG Flow for the nonlinear Sigma Model
Koerner, Daniel; Wipf, Andreas
2013-01-01
A study of the renormalization group flow in the three-dimensional nonlinear O(N) sigma model using Monte Carlo Renormalization Group (MCRG) techniques is presented. To achieve this, we combine an improved blockspin transformation with the canonical demon method to determine the flow diagram for a number of different truncations. Systematic errors of the approach are highlighted. Results are discussed with hindsight on the fixed point structure of the model and the corresponding critical exponents. Special emphasis is drawn on the existence of a nontrivial ultraviolet fixed point as required for theories modeling the asymptotic safety scenario of quantum gravity.
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Bagger, J.A.
1984-09-01
We begin to construct the most general supersymmetric Lagrangians in one, two and four dimensions. We find that the matter couplings have a natural interpretation in the language of the nonlinear sigma model.
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Mitev, Vladimir
2010-08-15
The purpose of this thesis is to deepen our understanding of the fundamental properties and defining features of non-linear sigma models on superspaces. We begin by presenting the major concepts that we have used in our investigation, namely Lie superalgebras and supergroups, non-linear sigma models and two dimensional conformal field theory. We then exhibit a method, called cohomological reduction, that makes use of the target space supersymmetry of non-linear sigma models to compute certain correlation functions. We then show how the target space supersymmetry of Ricci flat Lie supergroups simplifies the perturbation theory of suitable deformed Wess-Zumino-Witten models, making it possible to compute boundary conformal weights to all orders. This is then applied to the OSP (2S+2 vertical stroke 2S) Gross-Neveu Model, leading to a dual description in terms of the sigma model on the supersphere S{sup 2S+1} {sup vertical} {sup stroke} {sup 2S}. With this results in mind, we then turn to the similar, yet more intricate, theory of the non-linear sigma model on the complex projective superspaces CP{sup N-1} {sup vertical} {sup stroke} {sup N}. The cohomological reduction allows us to compute several important quantities non-perturbatively with the help of the system of symplectic fermions. Combining this with partial perturbative results for the whole theory, together with numerical computations, we propose a conjecture for the exact evolution of boundary conformal weights for symmetry preserving boundary conditions. (orig.)
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Gravitating $\\sigma$ Model Solitons
Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes with...
Gravitating $\\sigma$ Model Solitons
Kim, Y; Kim, Yoonbai; Moon, Sei-Hoon
1998-01-01
We study axially symmetric static solitons of O(3) nonlinear $\\sigma$ model coupled to (2+1)-dimensional anti-de Sitter gravity. The obtained solutions are not self-dual under static metric. The usual regular topological lump solution cannot form a black hole even though the scale of symmetry breaking is increased. There exist nontopological solitons of half integral winding in a given model, and the corresponding spacetimes involve charged Ba$\\tilde n$ados-Teitelboim-Zanelli black holes without non-Abelian scalar hair.
String Field Equations from Generalized Sigma Model
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Bardakci, K.; Bernardo, L.M.
1997-01-29
We propose a new approach for deriving the string field equations from a general sigma model on the world-sheet. This approach leads to an equation which combines some of the attractive features of both the renormalization group method and the covariant beta function treatment of the massless excitations. It has the advantage of being covariant under a very general set of both local and non-local transformations in the field space. We apply it to the tachyon, massless and first massive level, and show that the resulting field equations reproduce the correct spectrum of a left-right symmetric closed bosonic string.
Thermodynamics of O(N) sigma models : 1/N corrections
Andersen, JO; Boer, D; Warringa, HJ
2004-01-01
The thermodynamics of the O(N) linear and nonlinear sigma models in 3+1 dimensions is studied. We calculate the pressure to next-to-leading order in the 1/N expansion and show that at this order, temperature-independent renormalization is only possible at the minimum of the effective potential. The
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Candu, Constantin [Institut fuer Theoretische Physik, Zuerich (Switzerland); Mitev, Vladimir [Humboldt-Universitaet, Berlin (Germany). Inst. fuer Mathematik; Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Schomerus, Volker [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2013-08-15
We compute the complete 1-loop spectrum of anomalous dimensions for the bulk fields of non-linear sigma models on symmetric coset (super)spaces G/H, both with and without world-sheet supersymmetry. In addition, we provide two new methods for the construction of partition functions in the infinite radius limit and demonstrate their efficiency in the case of (super)sphere sigma models. Our results apply to a large number of target spaces including superspheres and superprojective spaces such as the N=2 sigma model on CP{sup 3} {sup vertical} {sup stroke} {sup 4}.
Gauging the Poisson sigma model
Zucchini, Roberto
2008-01-01
We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.
Spectra of conformal sigma models
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Tlapak, Vaclav
2015-04-15
In this thesis the spectra of conformal sigma models defined on (generalized) symmetric spaces are analysed. The spaces where sigma models are conformal without the addition of a Wess-Zumino term are supermanifolds, in other words spaces that include fermionic directions. After a brief review of the general construction of vertex operators and the background field expansion, we compute the diagonal terms of the one-loop anomalous dimensions of sigma models on semi-symmetric spaces. We find that the results are formally identical to the symmetric case. However, unlike for sigma models on symmetric spaces, off diagonal terms that lead to operator mixing are also present. These are not computed here. We then present a detailed analysis of the one-loop spectrum of the supersphere S{sup 3} {sup vertical} {sup stroke} {sup 2} sigma model as one of the simplest examples. The analysis illustrates the power and simplicity of the construction. We use this data to revisit a duality with the OSP(4 vertical stroke 2) Gross-Neveu model that was proposed by Candu and Saleur. With the help of a recent all-loop result for the anomalous dimension of (1)/(2)BPS operators of Gross-Neveu models, we are able to recover the entire zero-mode spectrum of the supersphere model. We also argue that the sigma model constraints and its equations of motion are implemented correctly in the Gross-Neveu model, including the one-loop data. The duality is further supported by a new all-loop result for the anomalous dimension of the ground states of the sigma model. However, higher-gradient operators cannot be completely recovered. It is possible that this discrepancy is related to a known instability of the sigma model. The instability of sigma models is due to symmetry preserving high-gradient operators that become relevant at arbitrarily small values of the coupling. This feature has been observed long ago in one-loop calculations of the O(N)-vector model and soon been realized to be a generic
Topological sigma models on supermanifolds
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Jia, Bei, E-mail: beijia@physics.utexas.edu
2017-02-15
This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of “superinstantons”. The language of supergeometry is used extensively throughout this paper.
Topological sigma models on supermanifolds
Jia, Bei
2017-02-01
This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of "superinstantons". The language of supergeometry is used extensively throughout this paper.
Topological Sigma Models On Supermanifolds
Jia, Bei
2016-01-01
This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of "superinstantons". The language of supergeometry is used extensively throughout this paper.
Bethe Ansatz in Stringy Sigma Models
Klose, T.; Zarembo, K.
2006-01-01
We compute the exact S-matrix and give the Bethe ansatz solution for three sigma-models which arise as subsectors of string theory in AdS(5)xS(5): Landau-Lifshitz model (non-relativistic sigma-model on S(2)), Alday-Arutyunov-Frolov model (fermionic sigma-model with su(1|1) symmetry), and Faddeev-Reshetikhin model (string sigma-model on S(3)xR).
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Chekhov, L.O.
1985-12-01
Matrix nonlinear sigma models are discussed and the matrix nonlinear sigma model in the case of N x ..cap alpha..N rectangular matrices is considered. The authors show that in two-dimensional Euclidean space, the model is renormalizable with respect to ..cap alpha.. and 1/N. The fulfillment of the chirality identity is demonstrated in the operator expansion for the renormalized theory.
The sausage sigma model revisited
Suneeta, Vardarajan
2014-01-01
Fateev's sausage sigma models in two and three dimensions are known to be integrable. We study their stability under RG flow in the target space by using results from the mathematics of Ricci flow. We show that the three dimensional sausage is unstable, whereas the two dimensional sausage appears to be stable at least at leading order as it approaches the sphere. The $n$-sphere, corresponding to the integrable O(n) sigma model, is geometrically stable and an attractor for nearby solutions to RG flow. We speculate that the stability results obtained seem to be linked to the classification of ancient solutions to Ricci flow (i.e., sigma models which are asymptotically free in the UV and nontrivial in the IR) in two and three dimensions. We also describe a class of perturbations of the three dimensional sausage (with the same continuous symmetries) which remarkably decouple. This indicates that there could be a new solution to RG flow which is described at least perturbatively as a deformation of the sausage.
Large-N Analysis of Three Dimensional Nonlinear Sigma Models
Higashijima, K; Tsuzuki, M; Higashijima, Kiyoshi; Itou, Etsuko; Tsuzuki, Makoto
2005-01-01
Non-perturbative renormalization group approach suggests that a large class of nonlinear sigma models are renormalizable in three dimensional space-time, while they are non-renormalizable in perturbation theory. ${\\cal N}=2$ supersymmetric nonlinear sigma models whose target spaces are Einstein-K\\"{a}hler manifolds with positive scalar curvature belongs to this class. hermitian symmetric spaces, being homogeneous, are specially simple examples of these manifolds. To find an independent evidence of the nonperturbative renormalizability of these models, the large N method, another nonperturbative method, is applied to 3-dimensional ${\\cal N}=2$ supersymmetric nonlinear sigma models on the target spaces $CP^{N-1}=SU(N)/[SU(N-1)\\times U(1)]$ and $Q^{N-2}=SO(N)/[SO(N-2)\\times SO(2)]$, two typical examples of hermitian symmetric spaces. We find that $\\beta$ functions in these models agree with the results of the nonperturbative renormalization group approach in the next-to-leading order of 1/N expansion, and have n...
Topological sigma models on supermanifolds
Directory of Open Access Journals (Sweden)
Bei Jia
2017-02-01
Full Text Available This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST operators and physical observables. Using supersymmetric localization, we express correlation functions in these theories as integrals over suitable supermanifolds. In the case of the A model, we obtain an integral over the supermoduli space of “superinstantons”. The language of supergeometry is used extensively throughout this paper.
Renormalized versions of the massless Thirring model
Casana, R
2003-01-01
We present a non-perturbative study of the (1+1)-dimensional massless Thirring model by using path integral methods. The model presents two features, one of them has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. We make a detailed analysis of their UV divergence structure, a non-perturbative regularization and renormalization processes are proposed.
Cohomological reduction of sigma models
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Candu, Constantin; Mitev, Vladimir; Schomerus, Volker [DESY, Hamburg (Germany). Theory Group; Creutzig, Thomas [North Carolina Univ., Chapel Hill, NC (United States). Dept. of Physics and Astronomy
2010-01-15
This article studies some features of quantum field theories with internal supersymmetry, focusing mainly on 2-dimensional non-linear sigma models which take values in a coset superspace. It is discussed how BRST operators from the target space super- symmetry algebra can be used to identify subsectors which are often simpler than the original model and may allow for an explicit computation of correlation functions. After an extensive discussion of the general reduction scheme, we present a number of interesting examples, including symmetric superspaces G/G{sup Z{sub 2}} and coset superspaces of the form G/G{sup Z{sub 4}}. (orig.)
On the Chiral Phase Transition in the Linear Sigma Model
Phat, T H; Hoa, L V; Phat, Tran Huu; Anh, Nguyen Tuan; Hoa, Le Viet
2004-01-01
The Cornwall-Jackiw-Tomboulis (CJT) effective action for composite operators at finite temperature is used to investigate the chiral phase transition within the framework of the linear sigma model as the low-energy effective model of quantum chromodynamics (QCD). A new renormalization prescription for the CJT effective action in the Hartree-Fock (HF) approximation is proposed. A numerical study, which incorporates both thermal and quantum effect, shows that in this approximation the phase transition is of first order. However, taking into account the higher-loop diagrams contribution the order of phase transition is unchanged.
Exploring the Supersymmetric $\\sigma$ Model
De Oliveira-Imbiriba, B C
1999-01-01
The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological nature, and its association with the torsion. It is also shown that to cancel the quantum conformal anomaly the model should obey the Einstein equations. We provide a quick introduction about supersymmetry in chapter 2 to help the understanding the supersymmetric extension of the model. In the last chapter we present the supersymmetric model and its equations of motion. Finally we work-out the two-supersymmetry case, introducing the chiral as well as the twisted chiral fields, expliciting the very specific $SU(2)\\otimes U(1)$ case.
The bi Hermitian topological sigma model
Zucchini, R
2006-01-01
BiHermitian geometry, discovered long ago by Gates, Hull and Roceck, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we work out the type A and B topological sigma models for a general biHermtian target space, we write down the explicit expression of the sigma model's action and BRST transformations and present a computation of the topological gauge fermion.
Geometry of Membrane Sigma Models
Vysoky, Jan
2015-01-01
String theory still remains one of the promising candidates for a unification of the theory of gravity and quantum field theory. One of its essential parts is relativistic description of moving multi-dimensional objects called membranes (or p-branes) in a curved spacetime. On the classical field theory level, they are described by an action functional extremalising the volume of a manifold swept by a propagating membrane. This and related field theories are collectively called membrane sigma models. Differential geometry is an important mathematical tool in the study of string theory. It turns out that string and membrane backgrounds can be conveniently described using objects defined on a direct sum of tangent and cotangent bundles of the spacetime manifold. Mathematical field studying such object is called generalized geometry. Its integral part is the theory of Leibniz algebroids, vector bundles with a Leibniz algebra bracket on its module of smooth sections. Special cases of Leibniz algebroids are better ...
Caldas, H C G
2001-01-01
Feynman's functional formulation of statistical mechanics is used to study the renormalizability of the well known Linear Chiral Sigma Model in the presence of fermionic fields at finite temperature in an alternative way. It is shown that the renormalization conditions coincide with those of the zero temperature model.
One Loop Renormalization of the Littlest Higgs Model
Grinstein, Benjamin; Uttayarat, Patipan
2011-01-01
In Little Higgs models a collective symmetry prevents the Higgs from acquiring a quadratically divergent mass at one loop. This collective symmetry is broken by weakly gauged interactions. Terms, like Yukawa couplings, that display collective symmetry in the bare Lagrangian are generically renormalized into a sum of terms that do not respect the collective symmetry except possibly at one renormalization point where the couplings are related so that the symmetry is restored. We study here the one loop renormalization of a prototypical example, the Littlest Higgs Model. Some features of the renormalization of this model are novel, unfamiliar form similar chiral Lagrangian studies.
Energy Technology Data Exchange (ETDEWEB)
Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica; INFN, Sezione di Torino (Italy)
2006-12-15
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics. (orig.)
VLES Modelling with the Renormalization Group
Institute of Scientific and Technical Information of China (English)
Chris De Langhe; Bart Merci; Koen Lodefier; Erik Dick
2003-01-01
In a Very-Large-Eddy Simulation (VLES), the filterwidth-wavenumber can be outside the inertial range, and simple subgrid models have to be replaced by more complicated ('RANS-like') models which can describe the transport of the biggest eddies. One could approach this by using a RANS model in these regions, and modify the lengthscale in the model for the LES-regions[1～3]. The problem with these approaches is that these models are specifically calibrated for RANS computations, and therefore not suitable to describe inertial range quantities. We investigated the construction of subgrid viscosity and transport equations without any calibrated constants, but these are calculated directly form the Navier-Stokes equation by means of a Renormalization Group (RG)procedure. This leads to filterwidth dependent transport equations and effective viscosity with the right limiting behaviour (DNS and RANS limits).
Functional renormalization group approach to the Kraichnan model.
Pagani, Carlo
2015-09-01
We study the anomalous scaling of the structure functions of a scalar field advected by a random Gaussian velocity field, the Kraichnan model, by means of functional renormalization group techniques. We analyze the symmetries of the model and derive the leading correction to the structure functions considering the renormalization of composite operators and applying the operator product expansion.
The biHermitian topological sigma model
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V. Irnerio 46, I-40126 Bologna (Italy); I.N.F.N., sezione di Bologna (Italy)
2006-12-15
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. By using the twisting procedure proposed by Kapustin and Li, we work out the type A and B topological sigma models for a general biHermtian target space, we write down the explicit expression of the sigma model's action and BRST transformations and present a computation of the topological gauge fermion and the topological action.
Higher-Dimensional Geometric $\\sigma$-Models
Vasilic, M
1999-01-01
Geometric $\\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\\sigma$-model by specifying the vacuum metric of the form $M^4\\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\\sigma$-model is suggested, which solves the above problem.
Generalized Kahler Geometry from supersymmetric sigma models
Bredthauer, A; Persson, J; Zabzine, M; Bredthauer, Andreas; Lindstrom, Ulf; Persson, Jonas; Zabzine, Maxim
2006-01-01
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
Dynamical real space renormalization group applied to sandpile models.
Ivashkevich, E V; Povolotsky, A M; Vespignani, A; Zapperi, S
1999-08-01
A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.
Two-Loop Renormalization in the Standard Model
Actis, S; Passarino, G; Passera, M
2006-01-01
In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles.
Renormalization of aperiodic model lattices: spectral properties
Kroon, L
2003-01-01
Many of the published results for one-dimensional deterministic aperiodic systems treat rather simplified electron models with either a constant site energy or a constant hopping integral. Here we present some rigorous results for more realistic mixed tight-binding systems with both the site energies and the hopping integrals having an aperiodic spatial variation. It is shown that the mixed Thue-Morse, period-doubling and Rudin-Shapiro lattices can be transformed to on-site models on renormalized lattices maintaining the individual order between the site energies. The character of the energy spectra for these mixed models is therefore the same as for the corresponding on-site models. Furthermore, since the study of electrons on a lattice governed by the Schroedinger tight-binding equation maps onto the study of elastic vibrations on a harmonic chain, we have proved that the vibrational spectra of aperiodic harmonic chains with distributions of masses determined by the Thue-Morse sequence and the period-doubli...
Energy Technology Data Exchange (ETDEWEB)
Chekhov, L.O.
1985-06-01
Matrix nonlinear sigma-model is considered in the case of rectangular matrices of the dimension Nx..alpha..N. Renormalizability of the model with respect to ..alpha.. and 1/N is demonstrated for the case of two-dimensional Euclidean space. Validity of the chiral identity is proved in the operator expansion for the renormalized theory.
Geometric sigma model of the Universe
Vasilić, Milovan
2017-05-01
The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model. Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity. Although they look like ordinary sigma models, they have the peculiarity that their complete matter content can be gauged away. The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory. The fact that background configuration is specified in advance is another peculiarity of geometric sigma models. In this paper, I construct geometric sigma models based on different background geometries of the Universe. Whatever background geometry is chosen, the dynamics of its small perturbations is shown to have a generic classical stability. This way, any freely chosen background metric is made a stable solution of a simple model. Three particular models of the Universe are considered as examples of how this is done in practice. Supported by Serbian Ministry of Education, Science and Technological Development (171031)
Six Sigma Driven Enterprise Model Transformation
Directory of Open Access Journals (Sweden)
Raymond Vella
2009-10-01
Full Text Available Enterprise architecture methods provide a structured system to understand enterprise activities. However, existing enterprise modelling methodologies take static views of the enterprise and do not naturally lead to a path of improvement during enterprise model transformation. This paper discusses the need for a methodology to facilitate changes for improvement in an enterprise. The six sigma methodology is proposed as the tool to facilitate progressive and continual Enterprise Model Transformation to allow businesses to adapt to meet increased customer expectation and global competition. An alignment of six sigma with phases of GERAM life cycle is described with inclusion of Critical-To-Satisfaction (CTS requirements. The synergies of combining the two methodologies are presented in an effort to provide a more culturally embedded framework for Enterprise Model Transformation that builds on the success of six sigma.
Disc instantons in linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Govindarajan, Suresh E-mail: suresh@chaos.iitm.ernet.in; Jayaraman, T. E-mail: jayaram@imsc.ernet.in; Sarkar, Tapobrata E-mail: tapo@theory.tifr.res.in
2002-12-16
We construct a linear sigma model for open-strings ending on special Lagrangian cycles of a Calabi-Yau manifold. We illustrate the construction for the cases considered by Aganagic and Vafa (AV). This leads naturally to concrete models for the moduli space of open-string instantons. These instanton moduli spaces can be seen to be intimately related to certain auxiliary boundary toric varieties. By considering the relevant Gelfand-Kapranov-Zelevinsky (GKZ) differential equations of the boundary toric variety, we obtain the contributions to the world volume superpotential on the A-branes from open-string instantons. By using an ansatz due to Aganagic, Klemm and Vafa (AKV), we obtain the relevant change of variables from the linear sigma model to the non-linear sigma model variables--the open-string mirror map. Using this mirror map, we obtain results in agreement with those of AV and AKV for the counting of holomorphic disc instantons.
Iterating block spin transformations of the O(3) nonlinear {sigma} model
Energy Technology Data Exchange (ETDEWEB)
Gottlob, A.P. [Fachbereich Physik, Universitaet Kaiserslautern, D-67653 Kaiserslautern (Germany); Hasenbusch, M. [DAMTP, Silver Street, Cambridge, CB3 9EW (England); Pinn, K. [Institut fuer Theoretische Physik I, Universitaet Muenster, Wilhelm-Klemm-Strasse 9, D-48149 Muenster (Germany)
1996-07-01
We study the iteration of block spin transformations in the O(3) symmetric nonlinear {sigma} model on a two-dimensional square lattice with the help of the Monte Carlo method. In contrast with the classical Monte Carlo renormalization group approach, we {ital do} attempt to explicitly compute the block spin effective actions. Using two different methods for the determination of effective couplings, we study the renormalization group flow for various parametrization and truncation schemes. The largest ansatz for the effective action contains thirteen coupling constants. Actions on the renormalized trajectory should describe theories with no lattice artifacts, even at a small correlation length. However, tests with the step scaling function of L{umlt u}scher, Weisz, and Wolff reveal that our truncated effective actions show sizable scaling violations indicating that the {ital Ans{umlt a}tze} are still too small. {copyright} {ital 1996 The American Physical Society.}
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
In part I and II of this series of papers all elements have been introduced to extend, to two loops, the set of renormalization procedures which are needed in describing the properties of a spontaneously broken gauge theory. In this paper, the final step is undertaken and finite renormalization is discussed. Two-loop renormalization equations are introduced and their solutions discussed within the context of the minimal standard model of fundamental interactions. These equations relate renormalized Lagrangian parameters (couplings and masses) to some input parameter set containing physical (pseudo-)observables. Complex poles for unstable gauge and Higgs bosons are used and a consistent setup is constructed for extending the predictivity of the theory from the Lep1 Z-boson scale (or the Lep2 WW scale) to regions of interest for LHC and ILC physics.
Two-Loop Renormalization in the Standard Model
Actis, S
2006-01-01
In part I general aspects of the renormalization of a spontaneously broken gauge theory have been introduced. Here, in part II, two-loop renormalization is introduced and discussed within the context of the minimal Standard Model. Therefore, this paper deals with the transition between bare parameters and fields to renormalized ones. The full list of one- and two-loop counterterms is shown and it is proven that, by a suitable extension of the formalism already introduced at the one-loop level, two-point functions suffice in renormalizing the model. The problem of overlapping ultraviolet divergencies is analyzed and it is shown that all counterterms are local and of polynomial nature. The original program of 't Hooft and Veltman is at work. Finite parts are written in a way that allows for a fast and reliable numerical integration with all collinear logarithms extracted analytically. Finite renormalization, the transition between renormalized parameters and physical (pseudo-)observables, will be discussed in p...
Sigma-models and Homotopy Algebras
Zeitlin, Anton M
2015-01-01
We review the relation between homotopy algebras of conformal field theory and geometric structures arising in sigma models. In particular we formulate conformal invariance conditions, which in the quasi-classical limit are Einstein equations with extra fields, as generalized Maurer-Cartan equations.
Nonlinear Reynolds stress models and the renormalization group
Rubinstein, Robert; Barton, J. Michael
1990-01-01
The renormalization group is applied to derive a nonlinear algebraic Reynolds stress model of anisotropic turbulence in which the Reynolds stresses are quadratic functions of the mean velocity gradients. The model results from a perturbation expansion that is truncated systematically at second order with subsequent terms contributing no further information. The resulting turbulence model applied to both low and high Reynolds number flows without requiring wall functions or ad hoc modifications of the equations. All constants are derived from the renormalization group procedure; no adjustable constants arise. The model permits inequality of the Reynolds normal stresses, a necessary condition for calculating turbulence-driven secondary flows in noncircular ducts.
The Renormalization of the Electroweak Standard Model to All Orders
Kraus, E
1998-01-01
We give the renormalization of the standard model of electroweak interactions to all orders of perturbation theory by using the method of algebraic renormalization, which is based on general properties of renormalized perturbation theory and not on a specific regularization scheme. The Green functions of the standard model are uniquely constructed to all orders, if one defines the model by the Slavnov-Taylor identity, Ward-identities of rigid symmetry and a specific form of the abelian local gauge Ward-identity, which continues the Gell-Mann Nishijima relation to higher orders. Special attention is directed to the mass diagonalization of massless and massive neutral vectors and ghosts. For obtaining off-shell infrared finite expressions it is required to take into account higher order corrections into the functional symmetry operators. It is shown, that the normalization conditions of the on-shell schemes are in agreement with the most general symmetry transformations allowed by the algebraic constraints.
Effective Charge on Polymer Colloids Obtained Using a Renormalization Model.
Quesada-Pérez; Callejas-Fernández; Hidalgo-Álvarez
1998-10-01
Static light scattering has been used to study the electrostatic interaction between colloidal particles. Experiments were carried out using a latex with a very small diameter, allowing structure determination at high particle concentration. The obtained effective charge characterizing this interaction is found to be smaller than the bare charge determined from titration. A renormalization model connecting both values has been used. The agreement between the renormalized charge and that obtained from scattering data seems to point out that this model operates well. Copyright 1998 Academic Press.
Sigma Models with Negative Curvature
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.
Non-Linear Sigma Model on Conifolds
Parthasarathy, R
2002-01-01
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\\"{a}hler metrics on these manifolds. The K\\"{a}hler 2-forms are found to be closed. The complex realization of these conifold metrics are used in the construction of 2-dimensional non-linear sigma model with the conifolds as target spaces. The action for the sigma model is shown to be bounded from below. By a suitable choice of the 'integration constants', arising in the solution of Ricci flatness requirement, the metric and the equations of motion are found to be {\\it{non-singular}}. As the target space is Ricci flat, the perturbative 1-loop counter terms being absent, the model becomes topological. The inherent U(1) fibre over the base of the conifolds is shown to correspond to a gauge connection in the sigma model. The same procedure is employed to construct the metric for the resolved conifold, in terms of complex coordinates and the action ...
Sigma-Model Solitons on Noncommutative Spaces
Dabrowski, Ludwik; Landi, Giovanni; Luef, Franz
2015-12-01
We use results from time-frequency analysis and Gabor analysis to construct new classes of sigma-model solitons over the Moyal plane and over noncommutative tori, taken as source spaces, with a target space made of two points. A natural action functional leads to self-duality equations for projections in the source algebra. Solutions, having nontrivial topological content, are constructed via suitable Morita duality bimodules.
Isobar Model for Photoproduction of K+Sigma0 and K0Sigma+ on the Proton
Mart, T
2005-01-01
Kaon photoproductions on the proton gamma p --> K+Sigma0 and gamma p --> K0Sigma+ have been simultaneously analyzed by using isobar models and new SAPHIR data. The result shows that isobar models such as KAON MAID require more resonances in order to explain the data.
Four loop renormalization of the Gross-Neveu model
Gracey, J A; Schroder, Y
2016-01-01
We renormalize the SU(N) Gross-Neveu model in the modified minimal subtraction (MSbar) scheme at four loops and determine the beta-function at this order. The theory ceases to be multiplicatively renormalizable when dimensionally regularized due to the generation of evanescent 4-fermi operators. The first of these appears at three loops and we correctly take their effect into account in deriving the renormalization group functions. We use the results to provide estimates of critical exponents relevant to phase transitions in graphene.
Model Companions of T_\\sigma for stable T
Baldwin, John; Shelah, Saharon
2001-01-01
Let T be a complete first order theory in a countable relational language L . We assume relation symbols have been added to make each formula equivalent to a predicate. Adjoin a new unary function symbol sigma to obtain the language L_sigma; T_sigma is obtained by adding axioms asserting that sigma is an L-automorphism. We provide necessary and sufficient conditions for T_sigma to have a model companion when T is stable. Namely, we introduce a new condition: T_sigma admits obstructions, and s...
On the renormalization group transformation for scalar hierarchical models
Energy Technology Data Exchange (ETDEWEB)
Koch, H. (Texas Univ., Austin (USA). Dept. of Mathematics); Wittwer, P. (Geneva Univ. (Switzerland). Dept. de Physique Theorique)
1991-06-01
We give a new proof for the existence of a non-Gaussian hierarchical renormalization group fixed point, using what could be called a beta-function for this problem. We also discuss the asymptotic behavior of this fixed point, and the connection between the hierarchical models of Dyson and Gallavotti. (orig.).
Brownian motion and parabolic Anderson model in a renormalized Poisson potential
Chen, Xia; Kulik, Alexey M.
2012-01-01
A method known as renormalization is proposed for constructing some more physically realistic random potentials in a Poisson cloud. The Brownian motion in the renormalized random potential and related parabolic Anderson models are modeled. With the renormalization, for example, the models consistent to Newton’s law of universal attraction can be rigorously constructed.
The role of hidden ambiguities in the linear sigma model with fermions
Energy Technology Data Exchange (ETDEWEB)
Hiller, Brigitte [Centro de Fisica Teorica, Departamento de Fisica da Universidade de Coimbra, 3004-516 Coimbra (Portugal); Mota, A.L. [Departamento de Ciencias Naturais, Universidade Federal de Sao Joao del Rei, Sao Joao del Rei, MG (Brazil) and Departamento de Fisica Moderna, Faculdad de Ciencias, Universidad de Granada, Granada (Spain)]. E-mail: motaal@ufsj.edu.br; Nemes, M.C. [Centro de Fisica Teorica, Departamento de Fisica da Universidade de Coimbra, 3004-516 Coimbra (Portugal); Departamento de Fisica, Instituto de Ciencias Exactas, Universidade Federal de Minas Gerais, BH, CEP 30161-970, MG (Brazil); Osipov, Alexander A. [Centro de Fisica Teorica, Departamento de Fisica da Universidade de Coimbra, 3004-516 Coimbra (Portugal); Joint Institute for Nuclear Research, Laboratory of Nuclear Problems, 141980 Dubna, Moscow Region (Russian Federation); Sampaio, Marcos [Departamento de Fisica, Instituto de Ciencias Exactas, Universidade Federal de Minas Gerais, BH, CEP 30161-970, MG (Brazil)
2006-04-17
The U{sub L}(3)xU{sub R}(3) linear sigma model (LSM) with quark degrees of freedom is used to show that radiative corrections generate undetermined finite contributions. Their origin is related to surface terms which are differences between divergent integrals with the same degree of divergence. The technique used to detect these ambiguities is an implicit regularization on basic divergent integrals that do not depend on external momenta. We show that such contributions are absorbed by renormalization or fixed by symmetry requirements. The general expression for surface terms is derived. Renormalization group coefficients are calculated, as well as relevant observables for this model, such as f{sub {pi}}, f{sub {kappa}} and the pion and kaon form factors.
Poisson sigma models and deformation quantization
Cattaneo, A S; Cattaneo, Alberto S.; Felder, Giovanni
2001-01-01
This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.
Renormalization-group calculation of excitation properties for impurity models
Yoshida, M.; Whitaker, M. A.; Oliveira, L. N.
1990-05-01
The renormalization-group method developed by Wilson to calculate thermodynamical properties of dilute magnetic alloys is generalized to allow the calculation of dynamical properties of many-body impurity Hamiltonians. As a simple illustration, the impurity spectral density for the resonant-level model (i.e., the U=0 Anderson model) is computed. As a second illustration, for the same model, the longitudinal relaxation rate for a nuclear spin coupled to the impurity is calculated as a function of temperature.
CP Violation in the Linear Sigma Model
Mizher, Ana Júlia
2009-01-01
Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the critical temperature.
CP Violation in the Linear Sigma Model
Mizher, Ana Júlia; Fraga, Eduardo S.
2008-01-01
Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the cr...
CP Violation in the Linear Sigma Model
Energy Technology Data Exchange (ETDEWEB)
Mizher, Ana Julia; Fraga, Eduardo S. [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972 (Brazil)
2009-04-01
Motivated by the possibility of the formation of CP-odd domains in heavy ion collisions, we investigate the effects of CP violation on the chiral transition within the linear sigma model with two flavors of quarks. We also study how the CP-odd system is affected by the presence of a strong magnetic field, that is presumably generated in a non-central heavy ion collision. We find that both ingredients play an important role, influencing drastically the nature of the phase transition and the critical temperature.
QCD strings as constrained grassmannian sigma model
Viswanathan, K S; Viswanathan, K S; Parthasarathy, R
1995-01-01
We present calculations for the effective action of string world sheet in R3 and R4 utilizing its correspondence with the constrained Grassmannian sigma model. Minimal surfaces describe the dynamics of open strings while harmonic surfaces describe that of closed strings. The one-loop effective action for these are calculated with instanton and anti-instanton background, reprsenting N-string interactions at the tree level. The effective action is found to be the partition function of a classical modified Coulomb gas in the confining phase, with a dynamically generated mass gap.
F-theory and linear sigma models
Bershadsky, M; Greene, Brian R; Johansen, A; Lazaroiu, C I
1998-01-01
We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the 4-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the `spectral bundle' and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad.
Constructive Renormalization of 2-dimensional Grosse-Wulkenhaar Model
Wang, Zhituo
2012-01-01
In this talk we briefly report the recent work on the construction of the 2-dimensional Grosse-Wulkenhaar model with the method of loop vertex expansion. We treat renormalization with this new tool, adapt Nelson's argument and prove Borel summability of the perturbation series. This is the first non-commutative quantum field theory model to be built in a non-perturbative sense.
Geometry and duality in Supersymmetric $\\sigma$-Models
Curtright, T L; Zachos, C K; Curtright, Thomas; Uematsu, Tsuneo; Zachos, Cosmas
1996-01-01
The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the Boson-Fermion Symphysis of the dual transition, and on the new geometry of the DSM.
Differential Poisson Sigma Models with Extended Supersymmetry
Arias, Cesar; Torres-Gomez, Alexander
2016-01-01
The induced two-dimensional topological N=1 supersymmetric sigma model on a differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a special case of the induced Poisson sigma model on the bi-graded supermanifold T[0,1]M. The bi-degree comprises the standard N-valued target space degree, corresponding to the form degree on the worldsheet, and an additional Z-valued fermion number, corresponding to the degree in the differential graded algebra of forms on M. The N=1 supersymmetry stems from the compatibility between the (extended) differential Poisson bracket and the de Rham differential on M. The latter is mapped to a nilpotent vector field Q of bi-degree (0,1) on T*[1,0](T[0,1]M), and the covariant Hamiltonian action is Q-exact. New extended supersymmetries arise as inner derivatives along special bosonic Killing vectors on M that induce Killing supervector fields of bi-degree (0,-1) on T*[1,0](T[0,1]M).
Beta-functions of non-linear $\\sigma$-models for disordered and interacting electron systems
Dell'Anna, Luca
2016-01-01
We provide and study complete sets of one-loop renormalization group equations, calculated at all orders in the interaction parameters, of several Finkel'stein non-linear $\\sigma$-models, the effective field theories describing the diffusive quantum fluctuations in correlated disordered systems. We consider different cases according to the presence of certain symmetries induced by the original random Hamiltonians, and we show that, for interacting systems, the Cartan's classification of symmetry classes is not enough to uniquely determine their scaling behaviors.
Real space renormalization group theory of disordered models of glasses.
Angelini, Maria Chiara; Biroli, Giulio
2017-03-28
We develop a real space renormalization group analysis of disordered models of glasses, in particular of the spin models at the origin of the random first-order transition theory. We find three fixed points, respectively, associated with the liquid state, with the critical behavior, and with the glass state. The latter two are zero-temperature ones; this provides a natural explanation of the growth of effective activation energy scale and the concomitant huge increase of relaxation time approaching the glass transition. The lower critical dimension depends on the nature of the interacting degrees of freedom and is higher than three for all models. This does not prevent 3D systems from being glassy. Indeed, we find that their renormalization group flow is affected by the fixed points existing in higher dimension and in consequence is nontrivial. Within our theoretical framework, the glass transition results in an avoided phase transition.
Renormalization of 3d quantum gravity from matrix models
Ambjørn, Jan; Loll, R
2004-01-01
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory of quantum gravity which predicts a positive cosmological constant. Since the approach is based on a sum over space-time histories, it is perturbatively non-renormalizable even in three dimensions. By mapping the three-dimensional theory to a two-matrix model with ABAB interaction we show that both the cosmological and the (perturbatively) non-renormalizable gravitational coupling constant undergo additive renormalizations consistent with canonical quantization.
Renormalization group approach to causal bulk viscous cosmological models
Energy Technology Data Exchange (ETDEWEB)
Belinchon, J A [Grupo Inter-Universitario de Analisis Dimensional, Dept. Fisica ETS Arquitectura UPM, Av. Juan de Herrera 4, Madrid (Spain); Harko, T [Department of Physics, University of Hong Kong, Pokfulam Road, Hong Kong (China); Mak, M K [Department of Physics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong (China)
2002-06-07
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the scaling properties of the gravitational field equations, the causal evolution equation of the bulk viscous pressure and the equations of state. The requirement of scale invariance imposes strong constraints on the temporal evolution of the bulk viscosity coefficient, temperature and relaxation time, thus leading to the possibility of obtaining the bulk viscosity coefficient-energy density dependence. For a cosmological model with bulk viscosity coefficient proportional to the Hubble parameter, we perform the analysis of the renormalization group flow around the scale-invariant fixed point, thereby obtaining the long-time behaviour of the scale factor.
F-theory and linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Bershadsky, M.; Johansen, A. [Harvard Univ., Cambridge, MA (United States). Lyman Lab. of Physics; Chiang, T.M. [Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, NY 14850 (United States); Greene, B.R.; Lazaroiu, C.I. [Departments of Physics and Mathematics, Columbia University, New York, NY 10027 (United States)
1998-09-07
We present an explicit method for translating between the linear sigma model and the spectral cover description of SU(r) stable bundles over an elliptically fibered Calabi-Yau manifold. We use this to investigate the four-dimensional duality between (0,2) heterotic and F-theory compactifications. We indirectly find that much interesting heterotic information must be contained in the `spectral bundle` and in its dual description as a gauge theory on multiple F-theory 7-branes. A by-product of these efforts is a method for analyzing semistability and the splitting type of vector bundles over an elliptic curve given as the sheaf cohomology of a monad. (orig.) 24 refs.
Tensor renormalization group analysis of CP(N-1) model
Kawauchi, Hikaru
2016-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of the CP($N-1$) model in the presence of the $\\theta$-term is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$. The numerical computation including the $\\theta$-term is left for future challenges.
Tensor renormalization group analysis of CP (N -1 ) model
Kawauchi, Hikaru; Takeda, Shinji
2016-06-01
We apply the higher-order tensor renormalization group to the lattice CP (N -1 ) model in two dimensions. A tensor network representation of the CP (N -1 ) model in the presence of the θ term is derived. We confirm that the numerical results of the CP(1) model without the θ term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region β ≫1 and that obtained by the Monte Carlo simulation in a wider range of β . The numerical computation including the θ term is left for future challenges.
A comparison of simulated precipitation by hybrid isentropic-sigma and sigma models
Johnson, Donald R.; Zapotocny, Tom H.; Reames, Fred M.; Wolf, Bart J.; Pierce, R. B.
1993-01-01
Simulations of dry and moist baroclinic development from 10- and 22-layer hybrid isentropic-sigma coordinate models are compared with those from 11-, 27-, and 35-layer sigma coordinate models. The ability of the models to transport water vapor and simulate equivalent potential temperature is examined. Predictions of the timing, location, and amount of precipitation are compared. Several analytical distributions of water vapor are specified initially. It is shown that when the relative humidity is vertically uniform through a substantial extent of the atmosphere, all the models produce very similar precipitation distributions. However, when water vapor is confined to relatively shallow layers, the ability of the sigma coordinate models to simulate the timing, location, and amount of precipitation is severely compromised.
Kaluza-Klein monopoles and gauged sigma-models
Bergshoeff, E; Janssen, B; Ortin, T; Alvarez-Gaumé, L.
1997-01-01
We propose an effective action for the eleven-dimensional (bosonic) Kaluza-Klein monopole solution. The construction of the action requires that the background fields admit an Abelian isometry group. The corresponding sigma-model is gauged with respect to this isometry. The gauged sigma-model is the
Kaluza-Klein Monopoles and Gauged Sigma Models
Bergshoeff, E.A.
1998-01-01
We review some aspects of branes. In particular, we discuss the worldvolume theory describing the dynamics of the Kaluza-Klein monopole which turns out to be a gauged sigma model. We also briefly review some recent applications of gauged sigma models to the worldvolume description of massive branes,
Mass Renormalization in the Nelson Model
Directory of Open Access Journals (Sweden)
Fumio Hiroshima
2017-01-01
Full Text Available The asymptotic behavior of the effective mass meff(Λ of the so-called Nelson model in quantum field theory is considered, where Λ is an ultraviolet cutoff parameter of the model. Let m be the bare mass of the model. It is shown that for sufficiently small coupling constant α of the model, meff(Λ/m can be expanded as meff(Λ/m=1+∑n=1∞an(Λα2n. A physical folklore is that an(Λ=O(logΛ(n-1 as Λ→∞. It is rigorously shown that 0
The sigma model on complex projective superspaces
Energy Technology Data Exchange (ETDEWEB)
Candu, Constantin; Mitev, Vladimir; Schomerus, Volker [DESY, Hamburg (Germany). Theory Group; Quella, Thomas [Amsterdam Univ. (Netherlands). Inst. for Theoretical Physics; Saleur, Hubert [CEA Saclay, 91 - Gif-sur-Yvette (France). Inst. de Physique Theorique; USC, Los Angeles, CA (United States). Physics Dept.
2009-08-15
The sigma model on projective superspaces CP{sup S-1} {sup vertical} {sup stroke} {sup S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle {theta}. Our main goal is to determine the spectrum of the model, non-perturbatively as a function of both parameters. We succeed to do so for all open boundary conditions preserving the full global symmetry of the model. In string theory parlor, these correspond to volume filling branes that are equipped with a monopole line bundle and connection. The paper consists of two parts. In the first part, we approach the problem within the continuum formulation. Combining combinatorial arguments with perturbative studies and some simple free field calculations, we determine a closed formula for the partition function of the theory. This is then tested numerically in the second part. There we propose a spin chain regularization of the CP{sup S-1} {sup vertical} {sup stroke} {sup S} model with open boundary conditions and use it to determine the spectrum at the conformal fixed point. The numerical results are in remarkable agreement with the continuum analysis. (orig.)
Renormalized dynamics of the Dean-Kawasaki model
Bidhoodi, Neeta; Das, Shankar P.
2015-07-01
We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ (x ,t ) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ . The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ ,θ } , linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D0 to DR is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997), 10.1007/s002570050396]. DR sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with DR=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.
Renormalized dynamics of the Dean-Kawasaki model.
Bidhoodi, Neeta; Das, Shankar P
2015-07-01
We study the model of a supercooled liquid for which the equation of motion for the coarse-grained density ρ(x,t) is the nonlinear diffusion equation originally proposed by Dean and Kawasaki, respectively, for Brownian and Newtonian dynamics of fluid particles. Using a Martin-Siggia-Rose (MSR) field theory we study the renormalization of the dynamics in a self-consistent form in terms of the so-called self-energy matrix Σ. The appropriate model for the renormalized dynamics involves an extended set of field variables {ρ,θ}, linked through a nonlinear constraint. The latter incorporates, in a nonperturbative manner, the effects of an infinite number of density nonlinearities in the dynamics. We show that the contributing element of Σ which renormalizes the bare diffusion constant D(0) to D(R) is same as that proposed by Kawasaki and Miyazima [Z. Phys. B Condens. Matter 103, 423 (1997)]. D(R) sharply decreases with increasing density. We consider the likelihood of a ergodic-nonergodic (ENE) transition in the model beyond a critical point. The transition is characterized by the long-time limit of the density correlation freezing at a nonzero value. From our analysis we identify an element of Σ which arises from the above-mentioned nonlinear constraint and is key to the viability of the ENE transition. If this self-energy would be zero, then the model supports a sharp ENE transition with D(R)=0 as predicted by Kawasaki and Miyazima. With the full model having nonzero value for this self-energy, the density autocorrelation function decays to zero in the long-time limit. Hence the ENE transition is not supported in the model.
Recursive renormalization group theory based subgrid modeling
Zhou, YE
1991-01-01
Advancing the knowledge and understanding of turbulence theory is addressed. Specific problems to be addressed will include studies of subgrid models to understand the effects of unresolved small scale dynamics on the large scale motion which, if successful, might substantially reduce the number of degrees of freedom that need to be computed in turbulence simulation.
On background-independent renormalization of spin foam models
Bahr, Benjamin
2014-01-01
In this article we discuss an implementation of renormalization group ideas to spin foam models, where there is no a priori length scale with which to define the flow. In the context of the continuum limit of these models, we show how the notion of cylindrical consistency of path integral measures gives a natural analogue of Wilson's RG flow equations for background-independent systems. We discuss the conditions for the continuum measures to be diffeomorphism-invariant, and consider both exact and approximate examples.
Ensemble renormalization group for the random-field hierarchical model.
Decelle, Aurélien; Parisi, Giorgio; Rocchi, Jacopo
2014-03-01
The renormalization group (RG) methods are still far from being completely understood in quenched disordered systems. In order to gain insight into the nature of the phase transition of these systems, it is common to investigate simple models. In this work we study a real-space RG transformation on the Dyson hierarchical lattice with a random field, which leads to a reconstruction of the RG flow and to an evaluation of the critical exponents of the model at T=0. We show that this method gives very accurate estimations of the critical exponents by comparing our results with those obtained by some of us using an independent method.
Duka, P; Zralek, M
2000-01-01
Quantization and renormalization of the left-right symmetric model is the main purpose of the paper. First the model at tree level with a Higgs sector containing one bidoublet and two triplets is precisely discussed. Then the canonical quantization and Faddeev-Popov Lagrangian are carried out ('t Hooft gauge). The BRST symmetry is discussed. Subsequently the on mass shell renormalization is performed and, as a test of consistency, the renormalization of the ZNiNj vertex is analyzed.
Tensor renormalization group approach to two-dimensional classical lattice models.
Levin, Michael; Nave, Cody P
2007-09-21
We describe a simple real space renormalization group technique for two-dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of the density matrix renormalization group method. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.
Perturbation theory for string sigma models
Bianchi, Lorenzo
2016-01-01
In this thesis we investigate quantum aspects of the Green-Schwarz superstring in various AdS backgrounds relevant for the AdS/CFT correspondence, providing several examples of perturbative computations in the corresponding integrable sigma-models. We start by reviewing in details the supercoset construction of the superstring action in $AdS_5 \\times S^5$, pointing out the limits of this procedure for $AdS_4$ and $AdS_3$ backgrounds. For the $AdS_4 \\times CP^3$ case we give a thorough derivation of an alternative action, based on the double-dimensional reduction of eleven-dimensional super-membranes. We then consider the expansion about the BMN vacuum and the S-matrix for the scattering of worldsheet excitations in the decompactification limit. To evaluate its elements efficiently we describe a unitarity-based method resulting in a very compact formula yielding the cut-constructible part of any one-loop two-dimensional S-matrix. In the second part of this review we analyze the superstring action on $AdS_4 \\ti...
A model for sigma factor competition in bacterial cells.
Mauri, Marco; Klumpp, Stefan
2014-10-01
Sigma factors control global switches of the genetic expression program in bacteria. Different sigma factors compete for binding to a limited pool of RNA polymerase (RNAP) core enzymes, providing a mechanism for cross-talk between genes or gene classes via the sharing of expression machinery. To analyze the contribution of sigma factor competition to global changes in gene expression, we develop a theoretical model that describes binding between sigma factors and core RNAP, transcription, non-specific binding to DNA and the modulation of the availability of the molecular components. The model is validated by comparison with in vitro competition experiments, with which excellent agreement is found. Transcription is affected via the modulation of the concentrations of the different types of holoenzymes, so saturated promoters are only weakly affected by sigma factor competition. However, in case of overlapping promoters or promoters recognized by two types of sigma factors, we find that even saturated promoters are strongly affected. Active transcription effectively lowers the affinity between the sigma factor driving it and the core RNAP, resulting in complex cross-talk effects. Sigma factor competition is not strongly affected by non-specific binding of core RNAPs, sigma factors and holoenzymes to DNA. Finally, we analyze the role of increased core RNAP availability upon the shut-down of ribosomal RNA transcription during the stringent response. We find that passive up-regulation of alternative sigma-dependent transcription is not only possible, but also displays hypersensitivity based on the sigma factor competition. Our theoretical analysis thus provides support for a significant role of passive control during that global switch of the gene expression program.
Renormalization group flow of scalar models in gravity
Energy Technology Data Exchange (ETDEWEB)
Guarnieri, Filippo
2014-04-08
In this Ph.D. thesis we study the issue of renormalizability of gravitation in the context of the renormalization group (RG), employing both perturbative and non-perturbative techniques. In particular, we focus on different gravitational models and approximations in which a central role is played by a scalar degree of freedom, since their RG flow is easier to analyze. We restrict our interest in particular to two quantum gravity approaches that have gained a lot of attention recently, namely the asymptotic safety scenario for gravity and the Horava-Lifshitz quantum gravity. In the so-called asymptotic safety conjecture the high energy regime of gravity is controlled by a non-Gaussian fixed point which ensures non-perturbative renormalizability and finiteness of the correlation functions. We then investigate the existence of such a non trivial fixed point using the functional renormalization group, a continuum version of the non-perturbative Wilson's renormalization group. In particular we quantize the sole conformal degree of freedom, which is an approximation that has been shown to lead to a qualitatively correct picture. The question of the existence of a non-Gaussian fixed point in an infinite-dimensional parameter space, that is for a generic f(R) theory, cannot however be studied using such a conformally reduced model. Hence we study it by quantizing a dynamically equivalent scalar-tensor theory, i.e. a generic Brans-Dicke theory with ω=0 in the local potential approximation. Finally, we investigate, using a perturbative RG scheme, the asymptotic freedom of the Horava-Lifshitz gravity, that is an approach based on the emergence of an anisotropy between space and time which lifts the Newton's constant to a marginal coupling and explicitly preserves unitarity. In particular we evaluate the one-loop correction in 2+1 dimensions quantizing only the conformal degree of freedom.
A non-perturbative real-space renormalization group scheme for the spin-1/2 XXX Heisenberg model
Degenhard, Andreas
1999-01-01
In this article we apply a recently invented analytical real-space renormalization group formulation which is based on numerical concepts of the density matrix renormalization group. Within a rigorous mathematical framework we construct non-perturbative renormalization group transformations for the spin-1/2 XXX Heisenberg model in the finite temperature regime. The developed renormalization group scheme allows for calculating the renormalization group flow behaviour in the temperature depende...
Dimensional reduction of Markov state models from renormalization group theory
Orioli, S.; Faccioli, P.
2016-09-01
Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.
Dimensional reduction of Markov state models from renormalization group theory.
Orioli, S; Faccioli, P
2016-09-28
Renormalization Group (RG) theory provides the theoretical framework to define rigorous effective theories, i.e., systematic low-resolution approximations of arbitrary microscopic models. Markov state models are shown to be rigorous effective theories for Molecular Dynamics (MD). Based on this fact, we use real space RG to vary the resolution of the stochastic model and define an algorithm for clustering microstates into macrostates. The result is a lower dimensional stochastic model which, by construction, provides the optimal coarse-grained Markovian representation of the system's relaxation kinetics. To illustrate and validate our theory, we analyze a number of test systems of increasing complexity, ranging from synthetic toy models to two realistic applications, built form all-atom MD simulations. The computational cost of computing the low-dimensional model remains affordable on a desktop computer even for thousands of microstates.
Comparing Poisson Sigma Model with A-model
Bonechi, F.; Cattaneo, A. S.; Iraso, R.
2016-10-01
We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.
Fine-tuning problem in renormalized perturbation theory: Spontaneously-broken gauge models
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-04-28
We study the stability of tree-level gauge hierarchies at higher orders in renormalized perturbation theory, in a model with spontaneously-broken gauge symmetries. We confirm previous results indicating that if the model is renormalized using BPHZ, then the tree-level hierarchy is not upset by the radiative corrections. Consequently, no fine-tuning of the initial parameters is required to maintain it, in contrast to the result obtained using Dimensional Renormalization. This verifies the conclusion that the need for fine-tuning, when it arises, is an artifact of the application of a certain class of renormalization schemes.
Renormalized New Solutions for the Massless Thirring Model
Casana, R.
We present a nonperturbative study of the (1+1)-dimensional massless Thirring model by using path integral methods. The regularization ambiguities — coming from the computation of the fermionic determinant — allow to find new solution types for the model. At quantum level the Ward identity for the 1PI 2-point function for the fermionic current separates such solutions in two phases or sectors, the first one has a local gauge symmetry that is implemented at quantum level and the other one without this symmetry. The symmetric phase is a new solution which is unrelated to the previous studies of the model and, in the nonsymmetric phase there are solutions that for some values of the ambiguity parameter are related to well-known solutions of the model. We construct the Schwinger-Dyson equations and the Ward identities. We make a detailed analysis of their UV divergence structure and, after, we perform a nonperturbative regularization and renormalization of the model.
Spatial dependence of entanglement renormalization in XY model
Usman, M.; Ilyas, Asif; Khan, Khalid
2017-09-01
In this article, a comparative study of the renormalization of entanglement in one-, two- and three-dimensional space and its relation with quantum phase transition (QPT) near the critical point is presented by implementing the quantum renormalization group (QRG) method using numerical techniques. Adopting the Kadanoff's block approach, numerical results for the concurrence are obtained for the spin {-}1/2 XY model in all the spatial dimensions. The results show similar qualitative behavior as we move from the lower to the higher dimensions in space, but the number of iterations reduces for achieving the QPT in the thermodynamic limit. We find that in the two-dimensional and three-dimensional spin {-}1/2 XY model, maximum value of the concurrence reduce by the factor of 1 / n (n=2,3) with reference to the maximum value of one-dimensional case. Moreover, we study the scaling behavior and the entanglement exponent. We compare the results for one-, two- and three-dimensional cases and illustrate how the system evolves near the critical point.
Real-space renormalization group approach to the Anderson model
Campbell, Eamonn
Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal
2016-01-01
In many models in condensed matter physics and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different consistent ways of regularizing and renormalizing quantum fluctuations, focusing on a symmetric energy cutoff scheme and dimensional regularization. We apply these techniques calculating the vacuum energy in the NJL model in 1+1 dimensions in the large-$N_c$ limit and the 3+1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
Consistent regularization and renormalization in models with inhomogeneous phases
Adhikari, Prabal; Andersen, Jens O.
2017-02-01
In many models in condensed matter and high-energy physics, one finds inhomogeneous phases at high density and low temperature. These phases are characterized by a spatially dependent condensate or order parameter. A proper calculation requires that one takes the vacuum fluctuations of the model into account. These fluctuations are ultraviolet divergent and must be regularized. We discuss different ways of consistently regularizing and renormalizing quantum fluctuations, focusing on momentum cutoff, symmetric energy cutoff, and dimensional regularization. We apply these techniques calculating the vacuum energy in the Nambu-Jona-Lasinio model in 1 +1 dimensions in the large-Nc limit and in the 3 +1 dimensional quark-meson model in the mean-field approximation both for a one-dimensional chiral-density wave.
The minimal linear sigma model for the Goldstone Higgs
Feruglio, Ferruccio; Kanshin, Kirill; Machado, Pedro Accioly Nogueira; Rigolin, Stefano; Saa, Sara
2016-01-01
In the context of the minimal SO(5) linear {\\sigma}-model, a complete renormalizable Lagrangian -including gauge bosons and fermions- is considered, with the symmetry softly broken to SO(4). The scalar sector describes both the electroweak Higgs doublet and the singlet {\\sigma}. Varying the {\\sigma} mass would allow to sweep from the regime of perturbative ultraviolet completion to the non-linear one assumed in models in which the Higgs particle is a low-energy remnant of some strong dynamics. We analyze the phenomenological implications and constraints from precision observables and LHC data. Furthermore, we derive the d <= 6 effective Lagrangian in the limit of heavy exotic fermions.
Strong parameter renormalization from optimum lattice model orbitals
Brosco, Valentina; Ying, Zu-Jian; Lorenzana, José
2017-01-01
Which is the best single-particle basis to express a Hubbard-like lattice model? A rigorous variational answer to this question leads to equations the solution of which depends in a self-consistent manner on the lattice ground state. Contrary to naive expectations, for arbitrary small interactions, the optimized orbitals differ from the noninteracting ones, leading also to substantial changes in the model parameters as shown analytically and in an explicit numerical solution for a simple double-well one-dimensional case. At strong coupling, we obtain the direct exchange interaction with a very large renormalization with important consequences for the explanation of ferromagnetism with model Hamiltonians. Moreover, in the case of two atoms and two fermions we show that the optimization equations are closely related to reduced density-matrix functional theory, thus establishing an unsuspected correspondence between continuum and lattice approaches.
Improved Nucleon Properties in the Extended Quark Sigma Model
Abu-Shady, M
2013-01-01
The quark sigma model describes the quarks interacting via exchange the pions and sigma meson fields. A new version of mesonic potential is suggested in the frame of some aspects of the quantum chromodynamics (QCD). The field equations have been solved in the mean-field approximation for the hedgehog baryon state. The obtained results are compared with previous works and other models. We conclude that the suggested mesonic potential successfully calculates nucleon properties.
N=2 supersymmetric sigma-models in AdS
Butter, Daniel
2011-01-01
We construct the most general N=2 supersymmetric nonlinear sigma-model in four-dimensional anti-de Sitter (AdS) space in terms of N=1 chiral superfields. The target space is shown to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field. A remarkable property of the sigma-model constructed is that the algebra of OSp(2|4) transformations is closed off the mass shell.
The optical model potential of the $\\Sigma$ hyperon in nuclear matter
Dabrowski, J; Rozynek, J.
2009-01-01
We present our attempts to determine the optical model potential $U_\\Sigma = V_\\Sigma -iW_\\Sigma$ of the $\\Sigma$ hyperon in nuclear matter. We analyze the following sources of information on $U_\\Sigma$: $\\Sigma N$ scattering, $\\Sigma^-$ atoms, and final state interaction of $\\Sigma$ hyperons in the $(\\pi,K^+)$ and $(K^-.\\pi)$ reactions on nuclear targets. We conclude that $V_\\Sigma$ is repulsive inside the nucleus and has a shallow a tractive pocket at the nuclear surface. These features of ...
A numerical study of the RG equation for the deformed O(3) nonlinear sigma model
Belardinelli, L.; Destri, C.; Onofri, E.
1995-02-01
The Renormalization Group equation describing the evolution of the metric of the nonlinear sigma model poses some nice mathematical problems involving functional analysis, differential geometry and numerical analysis. In this article we briefly report some results obtained from the numerical study of the solutions in the case of a two-dimensional target space (deformation of the O(3) σ-model In particular, our analysis shows that the so-called sausages define an attracting manifold in the U(1)-symmetric case, at one-loop level. Moreover, data from two-loop evolution are used to test the association (Fateev, Onofri and ALB. Zamolodchikov, Nucl. Phys. B 406 (1993) 521) between the so-called SSM η field theory and a certain U(1)-symmetric, factorized scattering theory (FST).
Zapotocny, Tom H.; Johnson, Donald R.; Reames, Fred M.
1993-01-01
In an initial effort in regional numerical weather prediction, results from the University of Wisconsin isentropic-sigma (UW theta-sigma) hybrid model and an 'identical' sigma model are compared. The two main objectives are to demonstrate the capability of the UW theta-sigma model for regional numerical weather prediction and to identify advantages of the hybrid model in simulating atmospheric water vapor transport and precipitation relative to the sigma model. The 72-h simulations produced by the two models extend over a region covering the western Pacific Ocean, North America, and the western Atlantic Ocean. The simulations begin at 0000 UTC 13 January 1979, a period during which an intense Chicago blizzard develops over the central United States. This period also includes the rapid development of a cyclone in the western Pacific Ocean. Results using the Global Weather Experiment (GWE) ECMWF level IIIB data as initial and verification data indicate that both models produce reasonable and similar 72-h simulations, with the UW theta-sigma model mass and momentum distributions being slightly more accurate than the sigma model. Of particular importance for the Chicago blizzard is that the UW theta-sigma model more accurately simulates water vapor transport northward from the Gulf of Mexico and westward from the Atlantic Ocean. As a result, the hybrid model more accurately simulates observed precipitation, especially over the northeastern U.S. and southeastern Canada.
Comparing Tensor Renormalization Group and Monte Carlo calculations for spin and gauge models
Meurice, Yannick; Liu, Yuzhi; Xiang, Tao; Xie, Zhiyuan; Yu, Ji-Feng; Unmuth-Yockey, Judah; Zou, Haiyuan
2013-01-01
We show that the Tensor Renormalization Group (TRG) method can be applied to O(N) spin models, principal chiral models and pure gauge theories (Z2, U(1) and SU(2)) on (hyper) cubic lattices. We explain that contrarily to some common belief, it is very difficult to write compact formulas expressing the blockspinning of lattice models. We show that in contrast to other approaches, the TRG formulation allows us to write exact blocking formulas with numerically controllable truncations. The basic reason is that the TRG blocking separates neatly the degrees of freedom inside the block and which are integrated over, from those kept to communicate with the neighboring blocks. We argue that the TRG is a method that can handle large volumes, which is crucial to approach quasi-conformal systems. The method can also get rid of some sign problems. We discuss recent results regarding the critical properties of the 2D O(2) nonlinear sigma model with complex beta and chemical potential. As some of these results appeared in ...
Comparing Poisson Sigma Model with A-model
Bonechi, Francesco; Iraso, Riccardo
2016-01-01
We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [arXiv:0706.3164], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge-fixed PSM action.
Renormalization procedure for random tensor networks and the canonical tensor model
Sasakura, Naoki
2015-01-01
We discuss a renormalization procedure for random tensor networks, and show that the corresponding renormalization-group flow is given by the Hamiltonian vector flow of the canonical tensor model, which is a discretized model of quantum gravity. The result is the generalization of the previous one concerning the relation between the Ising model on random networks and the canonical tensor model with N=2. We also prove a general theorem which relates discontinuity of the renormalization-group flow and the phase transitions of random tensor networks.
A topological sigma model of biKaehler geometry
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V. Irnerio 46, I-40126 Bologna (Italy); I.N.F.N., sezione di Bologna (Italy)
2006-01-15
BiKaehler geometry is characterized by a riemannian metric g{sub ab} and two covariantly constant generally non commuting complex structures K{sub {+-}}{sup a}{sub b}, with respect to which g{sub ab} is hermitean. It is a particular case of the bihermitean geometry of Gates, Hull and Roceck, the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. We present a sigma model for biKaehler geometry that is topological in the following sense: i) the action is invariant under a fermionic symmetry {delta}; ii) {delta} is nilpotent on shell; iii) the action is {delta}-exact on shell up to a topological term; iv) the resulting field theory depends only on a subset of the target space geometrical data. The biKaehler sigma model is obtainable by gauge fixing the Hitchin model with generalized Kaehler target space. It further contains the customary A topological sigma model as a particular case. However, it is not seemingly related to the (2,2) supersymmetric biKaehler sigma model by twisting in general.
A topological sigma model of biKaehler geometry
Zucchini, R
2006-01-01
BiKaehler geometry is characterized by a Riemannian metric g_{ab} and two covariantly constant generally non commuting complex structures K_+^a_b, K_-^a_b, with respect to which g_{ab} is Hermitian. It is a particular case of the biHermitian geometry of Gates, Hull and Roceck, the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. We present a sigma model for biKaehler geometry that is topological in the following sense: i) the action is invariant under a fermionic symmetry delta; ii) delta is nilpotent on shell; iii) the action is delta--exact on shell up to a topological term; iv) the resulting field theory depends only on a subset of the target space geometrical data. The biKaehler sigma model is obtainable by gauge fixing the Hitchin model with generalized Kaehler target space. It further contains the customary A topological sigma model as a particular case. However, it is not seemingly related to the (2,2) supersymmetric biKaehler sigma model by twisting in gener...
Two-loop renormalization in the standard model, part I. Prolegomena
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Actis, S. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Ferroglia, A. [Albert-Ludwigs-Univ., Freiburg (Germany). Fakultat fur Phys.]|[Zuerich Univ. (Switzerland). Inst. fuer Theoretische Physik; Passera, M. [Padua Univ. (Italy). Dipt. di Fisica]|[INFN, Sezione di Padova (Italy); Passarino, G. [Torino Univ. (Italy). Dipt. di Fisica Teorica]|[INFN, Sezione di Torino (Italy)
2006-12-15
In this paper the building blocks for the two-loop renormalization of the Standard Model are introduced with a comprehensive discussion of the special vertices induced in the Lagrangian by a particular diagonalization of the neutral sector and by two alternative treatments of the Higgs tadpoles. Dyson resummed propagators for the gauge bosons are derived, and two-loop Ward-Slavnov-Taylor identities are discussed. In part II, the complete set of counterterms needed for the two-loop renormalization will be derived. In part III, a renormalization scheme will be introduced, connecting the renormalized quantities to an input parameter set of (pseudo-)experimental data, critically discussing renormalization of a gauge theory with unstable particles. (orig.)
Quasicomplex N=2, d=1 Supersymmetric Sigma Models
Directory of Open Access Journals (Sweden)
Evgeny A. Ivanov
2013-11-01
Full Text Available We derive and discuss a new type of N=2 supersymmetric quantum mechanical sigma models which appear when the superfield action of the (1,2,1 multiplets is modified by adding an imaginary antisymmetric tensor to the target space metric, thus completing the latter to a non-symmetric Hermitian metric. These models are not equivalent to the standard de Rham sigma models, but are related to them through a certain special similarity transformation of the supercharges. On the other hand, they can be obtained by a Hamiltonian reduction from the complex supersymmetric N=2 sigma models built on the multiplets (2,2,0 and describing the Dolbeault complex on the manifolds with proper isometries. We study in detail the extremal two-dimensional case, when the target space metric is defined solely by the antisymmetric tensor, and show that the corresponding quantum systems reveal a hidden N=4 supersymmetry.
Yang–Baxter sigma models based on the CYBE
Directory of Open Access Journals (Sweden)
Takuya Matsumoto
2015-04-01
Full Text Available It is known that Yang–Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations have been characterized by classical r-matrices satisfying the modified classical Yang–Baxter equation (mCYBE. In this article, we propose the Yang–Baxter sigma models based on the classical Yang–Baxter equations (CYBE rather than the mCYBE. This generalization enables us to utilize various kinds of solutions of the CYBE to classify integrable deformations. In particular, it is straightforward to realize partial deformations of the target space without loss of the integrability of the parent theory.
Yang–Baxter sigma models based on the CYBE
Energy Technology Data Exchange (ETDEWEB)
Matsumoto, Takuya, E-mail: takuya.matsumoto@math.nagoya-u.ac.jp [Institute for Advanced Research and Department of Mathematics, Nagoya University, Nagoya 464-8602 (Japan); Yoshida, Kentaroh, E-mail: kyoshida@gauge.scphys.kyoto-u.ac.jp [Department of Physics, Kyoto University, Kyoto 606-8502 (Japan)
2015-04-15
It is known that Yang–Baxter sigma models provide a systematic way to study integrable deformations of both principal chiral models and symmetric coset sigma models. In the original proposal and its subsequent development, the deformations have been characterized by classical r-matrices satisfying the modified classical Yang–Baxter equation (mCYBE). In this article, we propose the Yang–Baxter sigma models based on the classical Yang–Baxter equations (CYBE) rather than the mCYBE. This generalization enables us to utilize various kinds of solutions of the CYBE to classify integrable deformations. In particular, it is straightforward to realize partial deformations of the target space without loss of the integrability of the parent theory.
Tensor renormalization group methods for spin and gauge models
Zou, Haiyuan
The analysis of the error of perturbative series by comparing it to the exact solution is an important tool to understand the non-perturbative physics of statistical models. For some toy models, a new method can be used to calculate higher order weak coupling expansion and modified perturbation theory can be constructed. However, it is nontrivial to generalize the new method to understand the critical behavior of high dimensional spin and gauge models. Actually, it is a big challenge in both high energy physics and condensed matter physics to develop accurate and efficient numerical algorithms to solve these problems. In this thesis, one systematic way named tensor renormalization group method is discussed. The applications of the method to several spin and gauge models on a lattice are investigated. theoretically, the new method allows one to write an exact representation of the partition function of models with local interactions. E.g. O(N) models, Z2 gauge models and U(1) gauge models. Practically, by using controllable approximations, results in both finite volume and the thermodynamic limit can be obtained. Another advantage of the new method is that it is insensitive to sign problems for models with complex coupling and chemical potential. Through the new approach, the Fisher's zeros of the 2D O(2) model in the complex coupling plane can be calculated and the finite size scaling of the results agrees well with the Kosterlitz-Thouless assumption. Applying the method to the O(2) model with a chemical potential, new phase diagram of the models can be obtained. The structure of the tensor language may provide a new tool to understand phase transition properties in general.
Renormalization group approach to a p-wave superconducting model
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Continentino, Mucio A.; Deus, Fernanda [Centro Brasileiro de Pesquisas Fisicas, Rua Dr. Xavier Sigaud, 150, Urca 22290-180, Rio de Janeiro, RJ (Brazil); Caldas, Heron [Departamento de Ciências Naturais, Universidade Federal de São João Del Rei, 36301-000, São João Del Rei, MG (Brazil)
2014-04-01
We present in this work an exact renormalization group (RG) treatment of a one-dimensional p-wave superconductor. The model proposed by Kitaev consists of a chain of spinless fermions with a p-wave gap. It is a paradigmatic model of great actual interest since it presents a weak pairing superconducting phase that has Majorana fermions at the ends of the chain. Those are predicted to be useful for quantum computation. The RG allows to obtain the phase diagram of the model and to study the quantum phase transition from the weak to the strong pairing phase. It yields the attractors of these phases and the critical exponents of the weak to strong pairing transition. We show that the weak pairing phase of the model is governed by a chaotic attractor being non-trivial from both its topological and RG properties. In the strong pairing phase the RG flow is towards a conventional strong coupling fixed point. Finally, we propose an alternative way for obtaining p-wave superconductivity in a one-dimensional system without spin–orbit interaction.
Controlling sign problems in spin models using tensor renormalization
Energy Technology Data Exchange (ETDEWEB)
Denbleyker, Alan [Iowa U.; Liu, Yuzhi [Colorado U.; Meurice, Y. [Iowa U.; Qin, M. P. [Beijing, Inst. Phys.; Xiang, T. [Beijing, Inst. Phys.; Xie, Z. Y. [Beijing, Inst. Phys.; Yu, J. F. [Beijing, Inst. Phys.; Zou, Haiyuan [Iowa U.
2014-01-09
We consider the sign problem for classical spin models at complex $\\beta =1/g_0^2$ on $L\\times L$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$\\beta$ than the reweighting Monte Carlo method. For the Ising model with complex $\\beta$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $L\\times L$ lattices when the number of states $D_s$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.
Density functionals and dimensional renormalization for an exactly solvable model
Kais, S.; Herschbach, D. R.; Handy, N. C.; Murray, C. W.; Laming, G. J.
1993-07-01
We treat an analytically solvable version of the ``Hooke's Law'' model for a two-electron atom, in which the electron-electron repulsion is Coulombic but the electron-nucleus attraction is replaced by a harmonic oscillator potential. Exact expressions are obtained for the ground-state wave function and electron density, the Hartree-Fock solution, the correlation energy, the Kohn-Sham orbital, and, by inversion, the exchange and correlation functionals. These functionals pertain to the ``intermediate'' density regime (rs≥1.4) for an electron gas. As a test of customary approximations employed in density functional theory, we compare our exact density, exchange, and correlation potentials and energies with results from two approximations. These use Becke's exchange functional and either the Lee-Yang-Parr or the Perdew correlation functional. Both approximations yield rather good results for the density and the exchange and correlation energies, but both deviate markedly from the exact exchange and correlation potentials. We also compare properties of the Hooke's Law model with those of two-electron atoms, including the large dimension limit. A renormalization procedure applied to this very simple limit yields correlation energies as good as those obtained from the approximate functionals, for both the model and actual atoms.
Block renormalization study on the nonequilibrium chiral Ising model.
Kim, Mina; Park, Su-Chan; Noh, Jae Dong
2015-01-01
We present a numerical study on the ordering dynamics of a one-dimensional nonequilibrium Ising spin system with chirality. This system is characterized by a direction-dependent spin update rule. Pairs of +- spins can flip to ++ or -- with probability (1-u) or to -+ with probability u while -+ pairs are frozen. The system was found to evolve into the ferromagnetic ordered state at any urenormalization analysis proposed by Basu and Hinrichsen [U. Basu and H. Hinrichsen, J. Stat. Mech.: Theor. Exp. (2011)]. The block renormalization method predicts, under the assumption of dynamic scale invariance, a scaling relation that can be used to estimate the scaling exponent numerically. We find the condition under which the scaling relation is justified. We then apply the method to our model and obtain the critical exponent zδ at several values of u. The numerical result is in perfect agreement with that of the previous study. This study serves as additional evidence for the claim that the nonequilibrium chiral Ising model displays power-law scaling behavior with continuously varying exponents.
Functional renormalization for antiferromagnetism and superconductivity in the Hubbard model
Energy Technology Data Exchange (ETDEWEB)
Friederich, Simon
2010-12-08
Despite its apparent simplicity, the two-dimensional Hubbard model for locally interacting fermions on a square lattice is widely considered as a promising approach for the understanding of Cooper pair formation in the quasi two-dimensional high-T{sub c} cuprate materials. In the present work this model is investigated by means of the functional renormalization group, based on an exact flow equation for the effective average action. In addition to the fermionic degrees of freedom of the Hubbard Hamiltonian, bosonic fields are introduced which correspond to the different possible collective orders of the system, for example magnetism and superconductivity. The interactions between bosons and fermions are determined by means of the method of ''rebosonization'' (or ''flowing bosonization''), which can be described as a continuous, scale-dependent Hubbard-Stratonovich transformation. This method allows an efficient parameterization of the momentum-dependent effective two-particle interaction between fermions (four-point vertex), and it makes it possible to follow the flow of the running couplings into the regimes exhibiting spontaneous symmetry breaking, where bosonic fluctuations determine the types of order which are present on large length scales. Numerical results for the phase diagram are presented, which include the mutual influence of different, competing types of order. (orig.)
A Mathematical Theory of the Gauged Linear Sigma Model
Fan, Huijun; Ruan, Yongbin
2015-01-01
We construct a rigorous mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete intersection X and the Landau-Ginzburg dual (FJRW-theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau-Ginzburg/Calabi-Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.
On quantum equivalence of dual $\\sigma$ models $SL(3)$ examples
Horváth, Z; Palla, L
1996-01-01
The equivalence of several $SL(3)$ sigma models and their special Abelian duals is investigated in the two loop order of perturbation theory. The investigation is based on extracting and comparing various $\\beta$ functions of the original and dual models. The role of the discrete global symmetries is emphasized.
On quantum equivalence of dual sigma models: SL(3) examples
Energy Technology Data Exchange (ETDEWEB)
Horvath, Z. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; Karp, R.L. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics; Palla, L. [Lorand Eoetvoes Univ., Budapest (Hungary). Inst. for Theoretical Physics
1997-04-14
The equivalence of several SL(3) sigma models and their special Abelian duals is investigated in two-loop order of perturbation theory. The investigation is based on extracting and comparing various {beta}-functions of the original and dual models. The role of discrete global symmetries is emphasized. (orig.).
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Renormalization-group theory for the eddy viscosity in subgrid modeling
Zhou, YE; Vahala, George; Hossain, Murshed
1988-01-01
Renormalization-group theory is applied to incompressible three-dimensional Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation now includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term. The renormalized eddy viscosity will not exhibit a cusp behavior if it is assumed that a spectral gap exists between the large and small scales.
Improved actions for the two-dimensional sigma-model
Caracciolo, Sergio; Montanari, Andrea; Pelissetto, Andrea
1997-01-01
For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an elementary plaquette. We show the large N solution and preliminary Monte Carlo results for N=3.
The Moduli Space in the Gauged Linear Sigma Model
Fan, Huijun; Ruan, Yongbin
2016-01-01
This is a survey article for the mathematical theory of Witten's Gauged Linear Sigma Model, as developed recently by the authors. Instead of developing the theory in the most general setting, in this paper we focus on the description of the moduli.
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
Ueda, K.; Otani, R.; Nishio, Y; Gendiar, A.; Nishino, T
2004-01-01
We report a way of obtaining a spin configuration snapshot, which is one of the representative spin configurations in canonical ensemble, in a finite area of infinite size two-dimensional (2D) classical lattice models. The corner transfer matrix renormalization group (CTMRG), a variant of the density matrix renormalization group (DMRG), is used for the numerical calculation. The matrix product structure of the variational state in CTMRG makes it possible to stochastically fix spins each by ea...
2D Poisson sigma models with gauged vectorial supersymmetry
Bonezzi, Roberto; Sundell, Per; Torres-Gomez, Alexander
2015-08-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
2D Poisson sigma models with gauged vectorial supersymmetry
Energy Technology Data Exchange (ETDEWEB)
Bonezzi, Roberto [Dipartimento di Fisica ed Astronomia, Università di Bologna and INFN, Sezione di Bologna,via Irnerio 46, I-40126 Bologna (Italy); Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-12
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
The Nonlinear Sigma Model With Distributed Adaptive Mesh Refinement
Liebling, S L
2004-01-01
An adaptive mesh refinement (AMR) scheme is implemented in a distributed environment using Message Passing Interface (MPI) to find solutions to the nonlinear sigma model. Previous work studied behavior similar to black hole critical phenomena at the threshold for singularity formation in this flat space model. This work is a follow-up describing extensions to distribute the grid hierarchy and presenting tests showing the correctness of the model.
2D Poisson sigma models with gauged vectorial supersymmetry
2015-01-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
2D Poisson Sigma Models with Gauged Vectorial Supersymmetry
Bonezzi, Roberto; Torres-Gomez, Alexander
2015-01-01
In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.
Redefining B twisted topological sigma models
Jonghe, F. de; Termonia, P.; Troost, W.; Vandoren, S.
2007-01-01
The recently proposed procedure to perform the topological B-twist in rigid N = 2 models is applied to the case of the o model on a Kähler manifold. This leads to an alternative description of Witten’s topological o model, which allows for a proper BRST interpretation and ghost number assignement. W
A heterotic sigma model with novel target geometry
Zucchini, Roberto
2011-01-01
We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.
Making Supersymmetric Quivers from N =(0,2) Sigma Models
Shifman, Mikhail; Yung, Alexei
2014-01-01
We show how to construct quiver-like (0,2) sigma models starting from n copies of (2,2) CP(N-1) models (or similar more generic models). These "quivers" present a natural generalization of the non-minimally deformed (2,2) model with an extra (0,2) fermion superfield on tangle bundle T[CP(N-1)xC^1] considered previously. A remarkable feature observed is elimination of the spontaneous supersymmetry breaking. We study supersymmetric vacua and determine the particle spectrum in the large-N limit. We then examine the \\beta -functions of our quiver-like (0,2) sigma models and show that under certain conditions they develop an infrared fixed point in the perturbative domain.
Nonlinear Sigma Models with Compact Hyperbolic Target Spaces
Gubser, Steven; Schoenholz, Samuel S; Stoica, Bogdan; Stokes, James
2015-01-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the $O(2)$ model. Unlike in the $O(2)$ case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggest...
Multi-Agent Modeling in Managing Six Sigma Projects
Directory of Open Access Journals (Sweden)
K. Y. Chau
2009-10-01
Full Text Available In this paper, a multi-agent model is proposed for considering the human resources factor in decision making in relation to the six sigma project. The proposed multi-agent system is expected to increase the acccuracy of project prioritization and to stabilize the human resources service level. A simulation of the proposed multiagent model is conducted. The results show that a multi-agent model which takes into consideration human resources when making decisions about project selection and project team formation is important in enabling efficient and effective project management. The multi-agent modeling approach provides an alternative approach for improving communication and the autonomy of six sigma projects in business organizations.
Linear Sigma Model Toolshed for D-brane Physics
Energy Technology Data Exchange (ETDEWEB)
Hellerman, Simeon
2001-08-23
Building on earlier work, we construct linear sigma models for strings on curved spaces in the presence of branes. Our models include an extremely general class of brane-worldvolume gauge field configurations. We explain in an accessible manner the mathematical ideas which suggest appropriate worldsheet interactions for generating a given open string background. This construction provides an explanation for the appearance of the derived category in D-brane physic complementary to that of recent work of Douglas.
Topological Twisted Sigma Model with H-flux Revisited
Energy Technology Data Exchange (ETDEWEB)
Chuang, Wu-yen
2006-08-18
In this paper we revisit the topological twisted sigma model with H-flux. We explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian geometry. we show that the resulting action consists of a BRST exact term and pullback terms, which only depend on one of the two generalized complex structures and the B-field. We then discuss the topological feature of the model.
Supersymmetric Q-Lumps in the Grassmannian nonlinear sigma models
Bak, D; Lee, J; Oh, P; Bak, Dongsu; Hahn, Sang-Ok; Lee, Joohan; Oh, Phillial
2007-01-01
We construct the N=2 supersymmetric Grassmannian nonlinear sigma model for the massless case and extend it to massive N=2 model by adding an appropriate superpotential. We then study their BPS equations leading to supersymmetric Q-lumps carrying both topological and Noether charges. These solutions are shown to be always time dependent even sometimes involving multiple frequencies. Thus we illustrate explicitly that the time dependence is consistent with remaining supersymmetries of solitons.
Renormalized parameters and perturbation theory in dynamical mean-field theory for the Hubbard model
Hewson, A. C.
2016-11-01
We calculate the renormalized parameters for the quasiparticles and their interactions for the Hubbard model in the paramagnetic phase as deduced from the low-energy Fermi-liquid fixed point using the results of a numerical renormalization-group calculation (NRG) and dynamical mean-field theory (DMFT). Even in the low-density limit there is significant renormalization of the local quasiparticle interaction U ˜, in agreement with estimates based on the two-particle scattering theory of J. Kanamori [Prog. Theor. Phys. 30, 275 (1963), 10.1143/PTP.30.275]. On the approach to the Mott transition we find a finite ratio for U ˜/D ˜ , where 2 D ˜ is the renormalized bandwidth, which is independent of whether the transition is approached by increasing the on-site interaction U or on increasing the density to half filling. The leading ω2 term in the self-energy and the local dynamical spin and charge susceptibilities are calculated within the renormalized perturbation theory (RPT) and compared with the results calculated directly from the NRG-DMFT. We also suggest, more generally from the DMFT, how an approximate expression for the q ,ω spin susceptibility χ (q ,ω ) can be derived from repeated quasiparticle scattering with a local renormalized scattering vertex.
The coupling of Poisson sigma models to topological backgrounds
Rosa, Dario
2016-01-01
We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical intrepretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.
The coupling of Poisson sigma models to topological backgrounds
Energy Technology Data Exchange (ETDEWEB)
Rosa, Dario [School of Physics, Korea Institute for Advanced Study,Seoul 02455 (Korea, Republic of)
2016-12-13
We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.
Generalized complex geometry, generalized branes and the Hitchin sigma model
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto E-mail: zucchinir@bo.infn.it
2005-03-01
Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a Batalin-Vilkovisky field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin-Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds. (author)
Generalized complex geometry, generalized branes and the Hitchin sigma model
Zucchini, R
2005-01-01
Hitchin's generalized complex geometry has been shown to be relevant in compactifications of superstring theory with fluxes and is expected to lead to a deeper understanding of mirror symmetry. Gualtieri's notion of generalized complex submanifold seems to be a natural candidate for the description of branes in this context. Recently, we introduced a field theoretic realization of generalized complex geometry, the Hitchin sigma model, extending the well known Poisson sigma model. In this paper, exploiting Gualtieri's formalism, we incorporate branes into the model. A detailed study of the boundary conditions obeyed by the world sheet fields is provided. Finally, it is found that, when branes are present, the classical Batalin--Vilkovisky cohomology contains an extra sector that is related non trivially to a novel cohomology associated with the branes as generalized complex submanifolds.
The coupling of Poisson sigma models to topological backgrounds
Rosa, Dario
2016-12-01
We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.
Sigma models for genuinely non-geometric backgrounds
Chatzistavrakidis, Athanasios; Lechtenfeld, Olaf
2015-01-01
The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.
On energy conversion in a sigma coordinate ocean model
Energy Technology Data Exchange (ETDEWEB)
Eldevik, Tor
1999-08-01
Energy diagnostics are useful for understanding the transfer of energy through instabilities and between different scales. In this note the conservation equations for kinetic and potential energy, divided into suitable mean and eddy quantities, for a sigma coordinate ocean model are set up. By identifying the transfer terms responsible for the conservative conversions between the different energies, an energy flow diagram is suggested. The motivation for this is twofold. Firstly, the average operator required for dividing the quantities of the flow into mean and eddy parts is in general not well defined in Cartesian coordinates when the upper and lower boundaries are not at fixed vertical levels. This is overcome by introducing the ''terrain-following'' sigma as the vertical coordinate. Secondly, and most important, many of today's numerical ocean models have this as the vertical coordinate. (author)
Off-shell BCJ Relation in Nonlinear Sigma Model
Chen, Gang; Liu, Hanqing
2016-01-01
We investigate relations among tree-level off-shell currents in nonlinear sigma model. Under Cayley parametrization, we propose and prove a general revised BCJ relation for even-point currents. Unlike the on-shell BCJ relation, the off-shell one behaves quite differently from Yang-Mills theory although the algebraic structure is the same. After performing the permutation summation in the revised BCJ relation, the sum is non-vanishing, instead, it equals to the sum of sub-current products with the BCJ coefficients under a specific ordering, which is presented by an explicit formula. Taking on-shell limit, this identity is reduced to the on-shell BCJ relation, and thus provides the full off-shell correspondence of tree-level BCJ relation in nonlinear sigma model.
Sigma-model soliton intersections from exceptional calibrations
Portugues, R
2002-01-01
A first-order `BPS' equation is obtained for 1/8 supersymmetric intersections of soliton-membranes (lumps) of supersymmetric (4+1)-dimensional massless sigma models, and a special non-singular solution is found that preserves 1/4 supersymmetry. For 4-dimensional hyper-K\\"ahler target spaces ($HK_4$) the BPS equation is shown to be the low-energy limit of the equation for a Cayley-calibrated 4-surface in $\\bE^4\\times HK_4$. Similar first-order equations are found for stationary intersections of Q-lump-membranes of the massive sigma model, but now generic solutions preserve either 1/8 supersymmetry or no supersymmetry, depending on the time orientation.
D-brane Solitons in Supersymmetric Sigma-Models
Gauntlett, J P; Tong, D; Townsend, P K; Gauntlett, Jerome P.; Portugues, Rubén; Tong, David; Townsend, Paul K.
2001-01-01
Massive D=4 N=2 supersymmetric sigma models typically admit domain wall (Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution in which a string ends on a wall, and show that it has an effective realization as a BIon of the D=4 super DBI-action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q-lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M-theory as calibrated, or `Q-calibrated', M5-branes in an M-monopole background.
Integrable deformations of T-dual $\\sigma$ models
Borsato, Riccardo
2016-01-01
We present a method to deform (generically non-abelian) T duals of two-dimensional $\\sigma$ models, which preserves classical integrability. The deformed models are identified by a linear operator $\\omega$ on the dualised subalgebra, which satisfies the 2-cocycle condition. We prove that the so-called homogeneous Yang-Baxter deformations are equivalent, via a field redefinition, to our deformed models when $\\omega$ is invertible. We explain the details for deformations of T duals of Principal Chiral Models, and present the corresponding generalisation to the case of supercoset models.
Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons
Nitta, M
2004-01-01
We present new non-Ricci-flat Kahler metrics with U(N) and O(N) isometries as target manifolds of conformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kahler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.
Electromagnetic axial anomaly in a generalized linear sigma model
Fariborz, Amir H.; Jora, Renata
2017-06-01
We construct the electromagnetic anomaly effective term for a generalized linear sigma model with two chiral nonets, one with a quark-antiquark structure, the other one with a four-quark content. We compute in the leading order of this framework the decays into two photons of six pseudoscalars: π0(137 ), π0(1300 ), η (547 ), η (958 ), η (1295 ) and η (1760 ). Our results agree well with the available experimental data.
Renormalization group approach to power-law modeling of complex metabolic networks.
Hernández-Bermejo, Benito
2010-08-07
In the modeling of complex biological systems, and especially in the framework of the description of metabolic pathways, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully understood at present. In order to provide additional insight in this sense, this article is devoted to the renormalization group analysis of reactions in fractal or self-similar media. In particular, the renormalization group methodology is applied to the investigation of how rate-laws describing such reactions are transformed when the geometric scale is changed. The precise purpose of such analysis is to investigate whether or not power-law rate-laws present some remarkable features accounting for the successes of power-law modeling. As we shall see, according to the renormalization group point of view the answer is positive, as far as power-laws are the critical solutions of the renormalization group transformation, namely power-law rate-laws are the renormalization group invariant solutions. Moreover, it is shown that these results also imply invariance under the group of concentration scalings, thus accounting for the reported power-law model accuracy over several orders of magnitude in metabolite concentrations. Copyright 2010 Elsevier Ltd. All rights reserved.
Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
Hori, Kentaro
2013-01-01
We systematically construct a class of two-dimensional $(2,2)$ supersymmetric gauged linear sigma models with phases in which a continuous subgroup of the gauge group is totally unbroken. We study some of their properties by employing a recently developed technique. The focus of the present work is on models with one K\\"ahler parameter. The models include those corresponding to Calabi-Yau threefolds, extending three examples found earlier by a few more, as well as Calabi-Yau manifolds of other dimensions and non-Calabi-Yau manifolds. The construction leads to predictions of equivalences of D-brane categories, systematically extending earlier examples. There is another type of surprise. Two distinct superconformal field theories corresponding to Calabi-Yau threefolds with different Hodge numbers, $h^{2,1}=23$ versus $h^{2,1}=59$, have exactly the same quantum K\\"ahler moduli space. The strong-weak duality plays a crucial r\\^ole in confirming this, and also is useful in the actual computation of the metric on t...
Can sigma models describe finite temperature chiral transitions?
Kocic, Aleksandar; Aleksandar KOCIC; John KOGUT
1995-01-01
Large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This is a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the absence of canonical scalar fields in the model. We point out that our results could be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.
Applying a Hybrid MCDM Model for Six Sigma Project Selection
Directory of Open Access Journals (Sweden)
Fu-Kwun Wang
2014-01-01
Full Text Available Six Sigma is a project-driven methodology; the projects that provide the maximum financial benefits and other impacts to the organization must be prioritized. Project selection (PS is a type of multiple criteria decision making (MCDM problem. In this study, we present a hybrid MCDM model combining the decision-making trial and evaluation laboratory (DEMATEL technique, analytic network process (ANP, and the VIKOR method to evaluate and improve Six Sigma projects for reducing performance gaps in each criterion and dimension. We consider the film printing industry of Taiwan as an empirical case. The results show that our study not only can use the best project selection, but can also be used to analyze the gaps between existing performance values and aspiration levels for improving the gaps in each dimension and criterion based on the influential network relation map.
Effective action and vacuum expectations in nonlinear $\\sigma$ model
Fayzullaev, B A
2015-01-01
The equations for effective action for nonlinear $\\sigma$ model are derived using DeWitt method in two forms - for generator of vertex parts $\\Gamma$ and for generator of weakly connected parts $W$. Loop-expansion solutions to these equations are found. It is shown that vacuum expectation values for various quantities including divergence of a N\\"{o}ther current, trace of the energy-momentum tensor and so on, can be calculated by this method. Also it is shown that vacuum expectation to the sigma-field is determined by an explicit combination of tree Green function and classical solution. It is shown that the limit when coupling constant tends to zero is singular one.
Effects of the Tsallis distribution in the linear sigma model
Ishihara, Masamichi
2014-01-01
The effects of the Tsallis distribution which has a parameter $q$ on physical quantities are studied using the linear sigma model in chiral phase transitions. The temperature dependences of the condensate and mass for various $q$ are shown, where the Tsallis distribution approaches the Boltzmann-Gibbs distribution as $q$ approaches $1$. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following facts are clarified. The chiral symmetry restoration for $q>1$ occurs at low temperature, compared with the restoration for $q=1$. The sigma mass and pion mass reflect the restoration. The critical temperature decreases monotonically as $q$ increases. The small deviation from the Boltzmann-Gibbs distribution results in the large deviations of physical quantities, especially the energy density. It is displayed from the energetic point of view that the small deviatio...
The two dimensional N=(2,2) Wess-Zumino Model in the Functional Renormalization Group Approach
Synatschke-Czerwonka, Franziska; Fischbacher, Thomas; Bergner, Georg
2010-01-01
We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called F...
Complex structure-induced deformations of sigma-models
Bykov, Dmitri
2016-01-01
We describe a deformation of the principal chiral model (with an even-dimensional target space G) by a B-field proportional to the K\\"ahler form on the target space. The equations of motion of the deformed model admit a zero-curvature representation. As a simplest example, we consider the case of G=S^1 x S^3. We also apply a variant of the construction to a deformation of the AdS_3 x S^3 x S^1 (super-)sigma-model.
Pion Effect of Nuclear Matter in a Chiral Sigma Model
Institute of Scientific and Technical Information of China (English)
HU Jin-niu; Y.Ogawa; H.Toki; A.Hosaka; SHEN Hong
2009-01-01
We develop a new framework for the study of the nuclear matter based on the linear sigma model.We introduce a completely new viewpoint on the treatment of the nuclear matter with the inclusion of the pion.We extend the relativistic chiral mean field model by using the similar method in the tensor optimized shell model.We also regulate the pion-nucleon interaction by considering the form-factor and short range repulsion effects.We obtain the equation of state of nuclear matter and study the importance of the pion effect.
Winding vacuum energies in a deformed O(4) sigma model
Bazhanov, Vladimir V; Lukyanov, Sergei L
2014-01-01
We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.
Winding vacuum energies in a deformed O(4) sigma model
Energy Technology Data Exchange (ETDEWEB)
Bazhanov, Vladimir V. [Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200 (Australia); Kotousov, Gleb A. [Department of Theoretical Physics, Research School of Physics and Engineering, Australian National University, Canberra, ACT 0200 (Australia); Lukyanov, Sergei L., E-mail: sergei@physics.rutgers.edu [NHETC, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855-0849 (United States); L.D. Landau Institute for Theoretical Physics, Chernogolovka 142432 (Russian Federation)
2014-12-15
We consider the problem of calculating the Casimir energies in the winding sectors of Fateev's SS-model, which is an integrable two-parameter deformation of the O(4) non-linear sigma model in two dimensions. This problem lies beyond the scope of all traditional methods of integrable quantum field theory including the thermodynamic Bethe ansatz and non-linear integral equations. Here we propose a solution based on a remarkable correspondence between classical and quantum integrable systems and express the winding energies in terms of certain solutions of the classical sinh-Gordon equation.
Nonlinear sigma models with compact hyperbolic target spaces
Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James
2016-06-01
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model [1, 2]. Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Quinto, A G
2016-01-01
We studied the Dynamical Symmetry Breaking (DSB) mechanism in a supersymmetric Chern-Simons theory in $\\left(2+1\\right)$ dimensions coupled to $N$ matter superfields in the superfield formalism. For this purpose, we developed a mechanism to calculate the effective superpotencial $K_{\\mathrm{eff}}\\left(\\sigma_{\\mathrm{cl}},\\alpha\\right)$, where $\\sigma_{\\mathrm{cl}}$ is a background superfield, and $\\alpha$ a gauge-fixing parameter that is introduced in the quantization process. The possible dependence of the effective potential on the gauge parameter have been studied in the context of quantum field theory. We developed the formalism of the Nielsen identities in the superfield language, which is the appropriate formalism to study DSB when the effective potential is gauge dependent. We also discuss how to calculate the effective superpotential via the Renormalization Group Equation (RGE) from the knowledge of the renormalization group functions of the theory, i.e., $\\beta$ functions and anomalous dimensions $\\...
Zhu; Yang
2000-06-01
A generalizing formulation of dynamical real-space renormalization that is appropriate for arbitrary spin systems is suggested. The alternative version replaces single-spin flipping Glauber dynamics with single-spin transition dynamics. As an application, in this paper we mainly investigate the critical slowing down of the Gaussian spin model on three fractal lattices, including nonbranching, branching, and multibranching Koch curves. The dynamical critical exponent z is calculated for these lattices using an exact decimation renormalization transformation in the assumption of the magneticlike perturbation, and a universal result z=1/nu is found.
Investigation of $\\eta'N$ system using linear sigma model
Sakai, Shuntaro
2016-01-01
In this paper, we investigate the $\\eta'N$ system using the three-flavor linear sigma model including the effect of the flavor SU(3) symmetry breaking. The $\\eta'N$ bound state is found also in the case including the flavor symmetry braking and the coupling with the $\\eta N$ and $\\pi N$ channels. The $\\eta'N$ interaction becomes more attractive with the inclusion of the flavor symmetry breaking which causes the mixing between the singlet and octet scalar mesons. The existence of such a bound state would have some impact on the $\\eta'$-nucleus system, which is of interest from the theoretical and experimental viewpoint.
A framework to a mass dimension one fermionic sigma model
Rogerio, R J Bueno; Pereira, S H; da Rocha, Roldao
2016-01-01
In this paper a mass dimension one fermionic sigma model, realized by the eigenspinors of the charge conjugation operator with dual helicity (Elko spinors), is developed. Such spinors are chosen as a specific realization of mass dimension one spinors, wherein the non-commutative fermionic feature is ruled by torsion. Moreover, we analyse Elko spinors as a source of matter in a background in expansion. Moreover, we analyse Elko spinors as a source of matter in a background in expansion and we have found that such kind of mass dimension one fermions can serve not only as dark matter but they also induce an effective cosmological constant.
SU(3) Polyakov Linear Sigma-Model in an External Magnetic Field
Tawfik, Abdel Nasser
2014-01-01
In the present work, we analyse the effects of an external magnetic field on the chiral critical temperature $T_c$ of strongly interacting matter. In doing this, we can characterize the magnetic properties of the quantum chromodynamics (QCD) strong interacting matter, the quark-gluon plasma (QGP). We investigate this in the framework of the SU(3) Polyakov linear sigma-model (PLSM). To this end, we implement two approaches representing two systems, in which the Polyakov-loop potential added to PLMS either renormalized or non-normalized. The effects of Landau quantization on the strongly interacting matter is conjectures to reduce the electromagnetic interactions between quarks. In this case, the color interactions will be dominant and increasing, which - in turn - can be achieved by increasing of the Polyakov-loop fields. Obviously, each of them equips us with a different understanding about the critical temperature under the effect of an external magnetic field. In both systems, we obtain a paramagnetic respo...
Chaotic Inflation from Nonlinear Sigma Models in Supergravity
Hellerman, Simeon; Yanagida, Tsutomu T
2014-01-01
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial K\\"ahler transformations are problematic to couple to supergravity. An additional field is necessary to make the K\\"ahler potential of the NLSM invariant in supergravity. This field must have a shift symmetry --- making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space $SU(3)/SU(2) \\times U(1)$, with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on $E_7/SO(10) \\times U(1) \\times U(1)$ which incorporates the first two ge...
Lectures on renormalization and asymptotic safety
Nagy, Sandor
2012-01-01
A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\\sigma$ model, the sine-Gordon model, and the model of quantum Einstein gravity. We also give a detailed analysis of infrared behavior of the models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure ...
Energy Technology Data Exchange (ETDEWEB)
Pruschke, T.; Bulla, R. [Institute fuer Theoretische Physik der Universitaet, Regensburg (Germany)
1995-05-01
The numerical renormalization group method is applied to an Anderson impurity with an energy dependent coupling to the conduction band. We describe how the discrete spectra resulting from the numerical calculation can be reliably smoothed using a continued fraction expansion. The investigations are connected with the study of models in infinite spatial dimensions.
Method of renormalization potential for one model of Hartree-Fock-Slater type
Zasorin, Y V
2002-01-01
A new method of the potential renormalization for the quasiclassical model of the Hartree-Fock-Slater real potential is proposed. The method makes it possible to easily construct the wave functions and contrary to the majority od similar methods it does not require the knowledge of the real-type potential
Ron, Dorit; Brandt, Achi; Swendsen, Robert H
2017-05-01
We present a surprisingly simple approach to high-accuracy calculations of the critical properties of the three-dimensional Ising model. The method uses a modified block-spin transformation with a tunable parameter to improve convergence in the Monte Carlo renormalization group. The block-spin parameter must be tuned differently for different exponents to produce optimal convergence.
Development and initial test of the University of Wisconsin global isentropic-sigma model
Zapotocny, Tom H.; Johnson, Donald R.; Reames, Fred M.
1994-01-01
The description of a global version of the University of Wisconsin (UW) hybrid isentropic-sigma (theta-sigma) model and the results from an initial numerical weather prediction experiment are presented in this paper. The main objectives of this initial test are to (1) discuss theta-sigma model development and computer requirements, (2) demonstrate the ability of the UW theta-sigma model for global numerical weather prediction using realistic orography and parameterized physical processes, and (3) compare the transport of an inert trace constituent against a nominally 'identical' sigma coordinate model. Initial and verifying data for the 5-day simulations presented in this work were supplied by the Goddard Earth Observing System (GEOS-1) data assimilation system. The time period studied is 1-6 February 1985. This validation experiment demonstrates that the global UW theta-sigma model produces a realistic 5-day simulation of the mass and momentum distributions when compared to both the identical sigma model and GEOS-1 verification. Root-mean-square errors demonstrate that the theta-sigma model is slightly more accurate than the nominally identical sigma model with respect to standard synoptic variables. Of particular importance, the UW theta-sigma model displays a distinct advantage over the conventional sigma model with respect to the prognostic simulation of inert trace constituent transport in amplifying baroclinic waves of the extratropics. This is especially true in the upper troposphere and stratosphere where the spatial integrity and conservation of an inert trace constituent is severely compromised in the sigma model compared to the theta-sigma model.
2D sigma models and differential Poisson algebras
Arias, Cesar; Boulanger, Nicolas; Sundell, Per; Torres-Gomez, Alexander
2015-08-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
2D sigma models and differential Poisson algebras
Arias, Cesar; Sundell, Per; Torres-Gomez, Alexander
2015-01-01
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
2D sigma models and differential Poisson algebras
Energy Technology Data Exchange (ETDEWEB)
Arias, Cesar [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Boulanger, Nicolas [Service de Mécanique et Gravitation, Université de Mons - UMONS,20 Place du Parc, 7000 Mons (Belgium); Laboratoire de Mathématiques et Physique Théorique,Unité Mixte de Recherche 7350 du CNRS, Fédération de Recherche 2964 Denis Poisson,Université François Rabelais, Parc de Grandmont, 37200 Tours (France); Sundell, Per [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Torres-Gomez, Alexander [Departamento de Ciencias Físicas, Universidad Andres Bello,Republica 220, Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile-UACh,Valdivia (Chile)
2015-08-18
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.
Semi-doubled Sigma Models for Five-branes
Kimura, Tetsuji
2015-01-01
We study two-dimensional ${\\cal N}=(2,2)$ gauge theory and its dualized system in terms of complex (linear) superfields and their alternatives. Although this technique itself is not new, we can obtain a new model, the so-called "semi-doubled" GLSM. Similar to doubled sigma model, this involves both the original and dual degrees of freedom simultaneously, whilst the latter only contribute to the system via topological interactions. Applying this to the ${\\cal N}=(4,4)$ GLSM for H-monopoles, i.e., smeared NS5-branes, we obtain its T-dualized systems in quite an easy way. As a bonus, we also obtain the semi-doubled GLSM for an exotic $5^3_2$-brane whose background is locally nongeometric. In the low energy limit, we construct the semi-doubled NLSM which also generates the conventional string worldsheet sigma models. In the case of the NLSM for $5^3_2$-brane, however, we find that the Dirac monopole equation does not make sense any more because the physical information is absorbed into the divergent part via the ...
SU($4$) Polyakov linear-sigma model at finite temperature and density
Diab, Abdel Magied; Tawfik, Abdel Nasser; Dahab, Eiman Abou El
2016-01-01
In mean-field approximation, the SU($4$) Polyakov linear - sigma model (PLSM) is constructed in order to characterize the quark-hadron phase structure in a wide range of temperatures and densities. The chiral condensates $\\sigma_l$, $\\sigma_s$ and $\\sigma_c$ for light, strange and charm quarks, respectively, and the deconfinement order-parameters $\\phi$ and $\\phi^*$ shall be analyzed at finite temperatures and densities. We conclude that the critical temperatures corresponding to charm condensates are greater than that to strange and light ones, respectively. Thus, the charm condensates are likely not affected by the QCD phase transition. Furthermore, increasing the chemical potentials decreases the corresponding critical temperatures.
Entanglement Renormalization and Wavelets.
Evenbly, Glen; White, Steven R
2016-04-08
We establish a precise connection between discrete wavelet transforms and entanglement renormalization, a real-space renormalization group transformation for quantum systems on the lattice, in the context of free particle systems. Specifically, we employ Daubechies wavelets to build approximations to the ground state of the critical Ising model, then demonstrate that these states correspond to instances of the multiscale entanglement renormalization ansatz (MERA), producing the first known analytic MERA for critical systems.
Nonlinear sigma models with compact hyperbolic target spaces
Energy Technology Data Exchange (ETDEWEB)
Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)
2016-06-23
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.
Mass splittings in $\\Sigma_b$ and $\\Sigma_b^*$
Rosner, Jonathan L.
2006-01-01
The charged $\\Sigma_b$ and $\\Sigma^*_b$ states have recently been reported by the CDF Collaboration. The relation of their reported charge-averaged masses to expectations based on the quark model is reviewed briefly. A relation is proved among the $\\Delta I = 1$ electromagnetic mass differences $\\Sigma_1 \\equiv M(\\Sigma^+) - M(\\Sigma^-)$, $\\Sigma^*_1 \\equiv M(\\Sigma^{*+})- M(\\Sigma^{*-})$, $\\Sigma_{b1} \\equiv M(\\Sigma_b^+) - M(\\Sigma_b^-)$, and $\\Sigma^*_{b1} \\equiv M(\\Sigma_b^{*+}) - M(\\Sigm...
Chaotic inflation from nonlinear sigma models in supergravity
Directory of Open Access Journals (Sweden)
Simeon Hellerman
2015-03-01
Full Text Available We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu–Goldstone boson (NGB of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry — making it a candidate for the inflaton (or axion. We give an explicit example of such a model for the coset space SU(3/SU(2×U(1, with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E7/SO(10×U(1×U(1 which incorporates the first two generations of (light quarks as the Nambu–Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here, including a connection to Witten–Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.
Chaotic inflation from nonlinear sigma models in supergravity
Hellerman, Simeon; Kehayias, John; Yanagida, Tsutomu T.
2015-03-01
We present a common solution to the puzzles of the light Higgs or quark masses and the need for a shift symmetry and large field values in high scale chaotic inflation. One way to protect, for example, the Higgs from a large supersymmetric mass term is if it is the Nambu-Goldstone boson (NGB) of a nonlinear sigma model. However, it is well known that nonlinear sigma models (NLSMs) with nontrivial Kähler transformations are problematic to couple to supergravity. An additional field is necessary to make the Kähler potential of the NLSM invariant in supergravity. This field must have a shift symmetry - making it a candidate for the inflaton (or axion). We give an explicit example of such a model for the coset space SU (3) / SU (2) × U (1), with the Higgs as the NGB, including breaking the inflaton's shift symmetry and producing a chaotic inflation potential. This construction can also be applied to other models, such as one based on E7 / SO (10) × U (1) × U (1) which incorporates the first two generations of (light) quarks as the Nambu-Goldstone multiplets, and has an axion in addition to the inflaton. Along the way we clarify and connect previous work on understanding NLSMs in supergravity and the origin of the extra field (which is the inflaton here), including a connection to Witten-Bagger quantization. This framework has wide applications to model building; a light particle from a NLSM requires, in supergravity, exactly the structure for chaotic inflaton or an axion.
Interpretation of topologically restricted measurements in lattice sigma-models
Bautista, Irais; Gerber, Urs; Hofmann, Christoph P; Mejía-Díaz, Héctor; Prado, Lilian
2014-01-01
We consider models with topological sectors, and difficulties with their Monte Carlo simulation. In particular we are concerned with the situation where a simulation has an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are possible only within single topological sectors. The challenge is to assemble such restricted measurements to obtain an approximation for the full-fledged result, which corresponds to the correct sampling over the entire set of configurations. Under certain conditions this is possible, and it provides in addition an estimate for the topological susceptibility chi_t. Moreover, the evaluation of chi_t might be feasible even from data in just one topological sector, based on the correlation of the topological charge density. Here we present numerical test results for these techniques in the framework of non-linear sigma-models.
Renormalization group flows and continual Lie algebras
Bakas, Ioannis
2003-01-01
We study the renormalization group flows of two-dimensional metrics in sigma models and demonstrate that they provide a continual analogue of the Toda field equations based on the infinite dimensional algebra G(d/dt;1). The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time. We provide the general solution of the renormalization group flows in terms of free fields, via Backlund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches...
Directory of Open Access Journals (Sweden)
A. Sadeghi
2007-03-01
Full Text Available Using both mean field renormalization group (MFRG and Surface-Bulk MFRG (SBMFRG, we study the critical behavior of the classical Heisenberg and XY models on a simple cubic lattice. Critical temperatures as well as critical exponents, characteristic the universality classes of these two models were calculated, analytically for1, 2, 3 and 4 spin clusters. The results are in good agreement with higher accurate methods such as Monte Carlo and High- temperature series.
Non-isometric T-duality from gauged sigma models
Chatzistavrakidis, Athanasios
2016-01-01
Local symmetries is one of the most successful themes in modern theoretical physics. Although they are usually associated to Lie algebras, a gradual increase of interest in more general situations where local symmetries are associated to groupoids and algebroids has taken place in recent years. On the other hand, dualities is another persistently interesting theme in modern physics. One of the most prominent examples is provided by target space duality in string theory. The latter, Abelian or not, is usually associated to the presence of isometries, which is however a very restrictive assumption. In this contribution we discuss some recent advances located at the intersection of the above two themes. Focusing on bosonic string sigma models we discuss certain gauged versions where (a) the invariance conditions on the background fields are much milder than the isometric case and (b) the gauge symmetry is generically associated to a Lie algebroid instead of just a Lie algebra. Furthermore we utilize such gauged ...
Poisson Sigma Model with branes and hyperelliptic Riemann surfaces
Ferrario, Andrea
2007-01-01
We derive the explicit form of the superpropagators in presence of general boundary conditions (coisotropic branes) for the Poisson Sigma Model. This generalizes the results presented in Cattaneo and Felder's previous works for the Kontsevich angle function used in the deformation quantization program of Poisson manifolds without branes or with at most two branes. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P_n with particular "alternating" boundary conditions. In presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero modes contributions.
Vainshtein mechanism in massive gravity nonlinear sigma models
Aoki, Katsuki
2016-01-01
We study the stability of the Vainshtein screening solution of the massive/bi-gravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius. The effective action is obtained by taking the $\\Lambda_2$ decoupling limit around a curved spacetime. First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only. This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massive/bi-gravity. Then to see the role of the excitation of the vector graviton, we study perturbations around the static and spherically symmetric solution obtained in bigravity explicitly. As a result, we find that linear excitations of the vector graviton cannot be helpful and the solution still suffers from a ghost and/or a gradient instability for any parameters of the theory for this background.
Linear $\\Sigma$ Model in the Gaussian Functional Approximation
Nakamura, I
2001-01-01
We apply a self-consistent relativistic mean-field variational ``Gaussian functional'' (or Hartree) approximation to the linear $\\sigma$ model with spontaneously and explicitly broken chiral O(4) symmetry. We set up the self-consistency, or ``gap'' and the Bethe-Salpeter equations. We check and confirm the chiral Ward-Takahashi identities, among them the Nambu-Goldstone theorem and the (partial) axial current conservation [CAC], both in and away from the chiral limit. With explicit chiral symmetry breaking we confirm the Dashen relation for the pion mass and partial CAC. We solve numerically the gap and Bethe-Salpeter equations, discuss the solutions' properties and the particle content of the theory.
TBA equations for excited states in the O(3) and O(4) nonlinear $\\sigma$-model
Balog, J.; Hegedus, A
2003-01-01
TBA integral equations are proposed for 1-particle states in the sausage- and SS-models and their $\\sigma$-model limits. Combined with the ground state TBA equations the exact mass gap is computed in the O(3) and O(4) nonlinear $\\sigma$-model and the results are compared to 3-loop perturbation theory and Monte Carlo data.
Scattering and duality in the 2 dimensional OSP(2|2) Gross Neveu and sigma models
Saleur, H
2009-01-01
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular a relation between this sigma model and the complex sine-Gordon model at a particular value of the coupling. We uncover an intriguing duality between the OSp(2|2) GN (resp. sigma) model on the one hand, and the SO(4) sigma (resp. GN model) on the other, somewhat generalizing to the massive case recent results on OSp(4|2). Finally, we write the TBA for the (SUSY version of the) flow into the random bond Ising model proposed by Cabra et al. [39], and conclude that their S matrix cannot be correct.
Supersymmetric O(N) models in d=3 with functional renormalization group (FRG) methods
Energy Technology Data Exchange (ETDEWEB)
Hellwig, Tobias; Heilmann, Marianne; Wipf, Andreas [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit Jena, Max-Wien-Platz 1, D-07743 Jena (Germany); Lithim, Daniel F. [Department of Physics and Astronomy, University of Sussex, BN1 9QH, Brighton (United Kingdom)
2013-07-01
While a lot of results concerning scalar O(N) models are known, much less is known for supersymmetric O(N) models. The 1/N expansions were examined in some earlier works with the help of the Hartree-Fock approximation. In this talk results for all N are presented. These results were obtained by using FRG methods and a manifest supersymmetric regulator. For finite N fixed point solutions and critical exponents are obtained. We comment on effects of different truncations in the effective average action. Starting point is the LPA approximation. In a second step a wave function renormalization is included and deviations from LPA solution are discussed. This is done for a field dependent and field independent form of the wave function renormalization. This knowledge could also prove to be helpful for further FRG studies of supersymmetric theories.
Two-Connection Renormalization and Nonholonomic Gauge Models of Einstein Gravity
Vacaru, Sergiu I
2009-01-01
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a metric structure, when gravitational models with infinite many couplings reduce to two-loop renormalizable effective actions. We use a key result from our partner work arXiv: 0902.0911 that the classical Einstein gravity theory can be reformulated equivalently as a nonholonomic gauge model in the bundle of affine/ de Sitter frames on pseudo-Riemannian spacetime. It is proven that (for a class of nonholonomic constraints and splitting of the Levi-Civita connection into a "renormalizable" distinguished connection, on a base background manifold, and a gauge like distorsion tensor, in total space) a nonholonomic differential renormalization procedure for quantum gravitational fields can be elaborated. Calculation labor is reduced to one- and two-loop levels and renormalization...
Thermodynamics of the two-dimensional XY model from functional renormalization
Jakubczyk, Pawel
2016-01-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the non-universal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on $\\phi^4$-type truncations. Our computation indicates that such an approximation is insufficient in the high-$T$ phase and a correct analysis of the specific heat profile requires account of an infinite number of interaction vertices.
Thermodynamics of the two-dimensional XY model from functional renormalization.
Jakubczyk, P; Eberlein, A
2016-06-01
We solve the nonperturbative renormalization-group flow equations for the two-dimensional XY model at the truncation level of the (complete) second-order derivative expansion. We compute the thermodynamic properties in the high-temperature phase and compare the nonuniversal features specific to the XY model with results from Monte Carlo simulations. In particular, we study the position and magnitude of the specific-heat peak as a function of temperature. The obtained results compare well with Monte Carlo simulations. We additionally gauge the accuracy of simplified nonperturbative renormalization-group treatments relying on ϕ^{4}-type truncations. Our computation indicates that such an approximation is insufficient in the high-T phase and a correct analysis of the specific-heat profile requires account of an infinite number of interaction vertices.
Hasenfratz, Anna
2010-01-01
Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.
Meloni, Davide; Riad, Stella
2014-01-01
In the context of non-supersymmetric SO(10) models, we analyze the renormalization group equations for the fermions (including neutrinos) from the GUT energy scale down to the electroweak energy scale, explicitly taking into account the effects of an intermediate energy scale induced by a Pati--Salam gauge group. To determine the renormalization group running, we use a numerical minimization procedure based on a nested sampling algorithm that randomly generates the values of 19 model parameters at the GUT scale, evolves them, and finally constructs the values of the physical observables and compares them to the existing experimental data at the electroweak scale. We show that the evolved fermion masses and mixings present sizable deviations from the values obtained without including the effects of the intermediate scale.
Meloni, Davide; Ohlsson, Tommy; Riad, Stella
2014-12-01
In the context of non-supersymmetric SO(10) models, we analyze the renormalization group equations for the fermions (including neutrinos) from the GUT energy scale down to the electroweak energy scale, explicitly taking into account the effects of an intermediate energy scale induced by a Pati-Salam gauge group. To determine the renormalization group running, we use a numerical minimization procedure based on a nested sampling algorithm that randomly generates the values of 19 model parameters at the GUT scale, evolves them, and finally constructs the values of the physical observables and compares them to the existing experimental data at the electroweak scale. We show that the evolved fermion masses and mixings present sizable deviations from the values obtained without including the effects of the intermediate scale.
Institute of Scientific and Technical Information of China (English)
何春山; 李志兵
2003-01-01
The correlation function of a two-dimensionalIsing model is calculated by the corner transfer matrix renormalization group method.We obtain the critical exponent η= 0.2496 with few computer resources.
Phase structure analysis of CP(N-1) model using Tensor renormalization group
Kawauchi, Hikaru
2016-01-01
The phase structure of the lattice CP($N-1$) model in two dimensions is analyzed by the tensor renormalization group (TRG) method. We focus on the case $N=2$ and compare the numerical result of the TRG method with that of the strong-coupling analysis in the presence of the $\\theta$ term and investigate the nature of the phase transition at $\\theta=\\pi$.
Scattering and duality in the 2 dimensional OSp(2|2) gross neveu and sigma models
Saleur, H.; Pozsgay, B.
2010-01-01
We write the thermodynamic Bethe ansatz for the massive OSp(2|2) Gross Neveu and sigma models. We find evidence that the GN S matrix proposed by Bassi and Leclair [12] is the correct one. We determine features of the sigma model S matrix, which seem highly unconventional; we conjecture in particular
Monte Carlo renormalization: the triangular Ising model as a test case.
Guo, Wenan; Blöte, Henk W J; Ren, Zhiming
2005-04-01
We test the performance of the Monte Carlo renormalization method in the context of the Ising model on a triangular lattice. We apply a block-spin transformation which allows for an adjustable parameter so that the transformation can be optimized. This optimization purportedly brings the fixed point of the transformation to a location where the corrections to scaling vanish. To this purpose we determine corrections to scaling of the triangular Ising model with nearest- and next-nearest-neighbor interactions by means of transfer-matrix calculations and finite-size scaling. We find that the leading correction to scaling just vanishes for the nearest-neighbor model. However, the fixed point of the commonly used majority-rule block-spin transformation appears to lie well away from the nearest-neighbor critical point. This raises the question whether the majority rule is suitable as a renormalization transformation, because the standard assumptions of real-space renormalization imply that corrections to scaling vanish at the fixed point. We avoid this inconsistency by means of the optimized transformation which shifts the fixed point back to the vicinity of the nearest-neighbor critical Hamiltonian. The results of the optimized transformation in terms of the Ising critical exponents are more accurate than those obtained with the majority rule.
Antonov, N. V.; Kakin, P. I.
2017-02-01
Applying the standard field theory renormalization group to the model of landscape erosion introduced by Pastor-Satorras and Rothman yields unexpected results: the model is multiplicatively renormalizable only if it involves infinitely many coupling constants (i.e., the corresponding renormalization group equations involve infinitely many β-functions). We show that the one-loop counterterm can nevertheless be expressed in terms of a known function V (h) in the original stochastic equation and its derivatives with respect to the height field h. Its Taylor expansion yields the full infinite set of the one-loop renormalization constants, β-functions, and anomalous dimensions. Instead of a set of fixed points, there arises a two-dimensional surface of fixed points that quite probably contains infrared attractive regions. If that is the case, then the model exhibits scaling behavior in the infrared range. The corresponding critical exponents turn out to be nonuniversal because they depend on the coordinates of the fixed point on the surface, but they satisfy certain universal exact relations.
Beyond the standard gauging: gauge symmetries of Dirac sigma models
Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa; Strobl, Thomas
2016-08-01
In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic σ-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac σ-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.
Ordered phase of the O(N) model within the nonperturbative renormalization group.
Peláez, Marcela; Wschebor, Nicolás
2016-10-01
We analyze nonperturbative renormalization group flow equations for the ordered phase of Z_{2} and O(N) invariant scalar models. This is done within the well-known derivative expansion scheme. For its leading order [local potential approximation (LPA)], we show that not every regulator yields a smooth flow with a convex free energy and discuss for which regulators the flow becomes singular. Then we generalize the known exact solutions of smooth flows in the "internal" region of the potential and exploit these solutions to implement an improved numerical algorithm, which is much more stable than previous ones for N>1. After that, we study the flow equations at second order of the derivative expansion and analyze how and when the LPA results change. We also discuss the evolution of the field renormalization factors.
Renormalization Group and Decoupling in Curved Space II. The Standard Model and Beyond
Gorbar, E V; Gorbar, Eduard V.; Shapiro, Ilya L.
2003-01-01
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The QCD sector at low-energies is described in terms of the composite effective fields. For fermions and scalars the massless limit shows perfect correspondence with the conformal anomaly, but similar limit in a massive vector case requires an extra compensating scalar. In all three cases the decoupling goes smoothly and monotonic. A particularly interesting case is the renormalization group flow in the theory with broken supersymmetry, where the sign of one of the beta-functions changes on the way from the UV to IR.
Charge Quantization in the CP(1) Nonlinear Sigma-Model
Hellerman, Simeon; Yanagida, Tsutomu T
2013-01-01
We investigate the consistency conditions for matter fields coupled to the four-dimensional (N = 1 supersymmetric) CP(1) nonlinear sigma model (the coset space SU(2)_G/U(1)_H). We find that consistency requires that the U(1)_H charge of the matter be quantized, in units of half of the U(1)_H charge of the Nambu-Goldstone (NG) boson, if the matter has a nonsingular kinetic term and the dynamics respect the full group SU(2)_G. We can then take the linearly realized group U(1)_H to comprise the weak hypercharge group U(1)_Y of the Standard Model. Thus we have charge quantization without a Grand Unified Theory (GUT), completely avoiding problems like proton decay, doublet-triplet splitting, and magnetic monopoles. We briefly investigate the phenomenological implications of this model-building framework. The NG boson is fractionally charged and completely stable. It can be naturally light, avoiding constraints while being a component of dark matter or having applications in nuclear physics. We also comment on the ...
Gund, Tamara M; Floyd, Jie; Jung, Dawoon
2004-01-01
We have performed molecular modeling studies on several sigma 1 specific ligands, including PD144418, spipethiane, haloperidol, pentazocine, and others to develop a pharmacophore for sigma 1 receptor-ligand binding, under the assumption that all the compounds interact at the same receptor binding site. The modeling studies have investigated the conformational and electrostatic properties of the ligands. Superposition of active molecules gave the coordinates of the hypothetical 5-point sigma 1 pharmacophore, as follows: R1 (0.85, 7.26, 0.30); R2 (5.47, 2.40, -1.51); R3 (-2.57, 4.82, -7.10); N (-0.71, 3.29, -6.40); carbon centroid (3.16, 4.83, -0.60), where R1, R2 were constructed onto the aromatic ring of each compound to represent hydrophobic interactions with the receptor; and R3 represents a hydrogen bond between the nitrogen atom and the receptor. Additional analyses were used to describe secondary binding sites to electronegative groups such as oxygen or sulfur atom. Those coordinates are (2.34, 5.08, -4.18). The model was verified by fitting other sigma 1 receptor ligands. This model may be used to search conformational databases for other possibly active ligands. In conjunction with rational drug design techniques the model may be useful in design and synthesis of novel sigma 1 ligands of high selectivity and potency. Calculations were performed using Sybyl 6.5.
Tensor renormalization group analysis of ${\\rm CP}(N-1)$ model in two dimensions
Kawauchi, Hikaru
2015-01-01
We apply the higher order tensor renormalization group to lattice CP($N-1$) model in two dimensions. A tensor network representation of CP($N-1$) model is derived. We confirm that the numerical results of the CP(1) model without the $\\theta$-term using this method are consistent with that of the O(3) model which is analyzed by the same method in the region $\\beta \\gg 1$ and that obtained by Monte Carlo simulation in a wider range of $\\beta$.
An ABET assessment model using Six Sigma methodology
Lalovic, Mira
Technical fields are changing so rapidly that even the core of an engineering education must be constantly reevaluated. Graduates of today give more dedication and, almost certainly, more importance to continued learning than to mastery of specific technical concepts. Continued learning shapes a high-quality education, which is what an engineering college must offer its students. The question is how to guarantee the quality of education. In addition, the Accreditation Board of Engineering and Technology is asking that universities commit to continuous and comprehensive education, assuming quality of the educational process. The research is focused on developing a generic assessment model for a college of engineering as an annual cycle that consists of a systematic assessment of every course in the program, followed by an assessment of the program and of the college as a whole using Six Sigma methodology. This unique approach to assessment in education will provide a college of engineering with valuable information regarding many important curriculum decisions in every accreditation cycle. The Industrial and Manufacturing Engineering (IME) Program in the College of Engineering at the University of Cincinnati will be used as a case example for a preliminary test of the generic model.
Low-energy limit of the extended Linear Sigma Model
Divotgey, Florian; Giacosa, Francesco; Rischke, Dirk H
2016-01-01
The extended Linear Sigma Model (eLSM) is an effective hadronic model based on the linear realization of chiral symmetry $SU(N_f)_L \\times SU(N_f)_R$, with (pseudo)scalar and (axial-)vector mesons as degrees of freedom. In this paper, we study the low-energy limit of the eLSM for $N_f=2$ flavors by integrating out all fields except for the pions, the (pseudo-)Nambu--Goldstone bosons of chiral symmetry breaking. We only keep terms entering at tree level and up to fourth order in powers of derivatives of the pion fields. Up to this order, there are four low-energy coupling constants in the resulting low-energy effective action. We show that the latter is formally identical to Chiral Perturbation Theory (ChPT), after choosing a representative for the coset space generated by chiral symmetry breaking and expanding up to fourth order in powers of derivatives of the pion fields. Two of the low-energy coupling constants of the eLSM are uniquely determined by a fit to hadron masses and decay widths. We find that thei...
Altered Sigma-1 Receptor Expression in Two Animal Models of Cognitive Impairment
Kuzhuppilly Ramakrishnan, Nisha; Marosi, Krisztina; Nyakas, Csaba J.; Kwizera, Chantal; Elsinga, Philip H.; Ishiwata, Kiichi; Luiten, Paul G M; Dierckx, Rudi A. J. O.; van Waarde, Aren
PURPOSE: Sigma-1 receptors are involved in learning and memory processes. We assessed sigma-1 receptor expression and memory function in two animal models of cognitive impairment. PROCEDURES: Male Wistar-Hannover rats were either lesioned by unilateral injection of N-methyl-D-aspartic acid in the
Altered Sigma-1 Receptor Expression in Two Animal Models of Cognitive Impairment
Kuzhuppilly Ramakrishnan, Nisha; Marosi, Krisztina; Nyakas, Csaba J.; Kwizera, Chantal; Elsinga, Philip H.; Ishiwata, Kiichi; Luiten, Paul G M; Dierckx, Rudi A. J. O.; van Waarde, Aren
2015-01-01
PURPOSE: Sigma-1 receptors are involved in learning and memory processes. We assessed sigma-1 receptor expression and memory function in two animal models of cognitive impairment. PROCEDURES: Male Wistar-Hannover rats were either lesioned by unilateral injection of N-methyl-D-aspartic acid in the nu
Tokuyama, Michio
2017-01-01
The renormalized simplified model is proposed to investigate indirectly how the static structure factor plays an important role in renormalizing a quadratic nonlinear term in the ideal mode-coupling memory function near the glass transition. The renormalized simplified recursion equation is then derived based on the time-convolutionless mode-coupling theory (TMCT) proposed recently by the present author. This phenomenological approach is successfully applied to check from a unified point of view how strong liquids are different from fragile liquids. The simulation results for those two types of liquids are analyzed consistently by the numerical solutions of the recursion equation. Then, the control parameter dependence of the renormalized nonlinear exponent in both types of liquids is fully investigated. Thus, it is shown that there exists a novel difference between the universal behavior in strong liquids and that in fragile liquids not only for their transport coefficients but also for their dynamics.
Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
Chatzistavrakidis, Athanasios; Jonke, Larisa; Strobl, Thomas
2016-01-01
In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic sigma-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field th...
A Renormalization Group Like Model for a Democratic Dictatorship
Galam, Serge
2015-03-01
We review a model of sociophysics which deals with democratic voting in bottom up hierarchical systems. The connection to the original physical model and technics are outlined underlining both the similarities and the differences. Emphasis is put on the numerous novel and counterintuitive results obtained with respect to the associated social and political framework. Using this model a real political event was successfully predicted with the victory of the French extreme right party in the 2000 first round of French presidential elections. The perspectives and the challenges to make sociophysics a predictive solid field of science are discussed.
O(3) Non-linear $\\sigma$ model with Hopf term and Higher spin theories
Govindarajan, T R; Shaji, N; Sivakumar, M
1993-01-01
Following our earlier work we argue in detail for the equivalence of the nonlinear $\\sigma$ model with Hopf term at~$\\theta=\\pi/2s$ ~and an interacting spin-s theory. We give an ansatz for spin-s operators in the $\\sigma$ model and show the equivalence of the correlation functions.We also show the relation between topological and Noether currents. We obtain the Lorentz and discrete transformation properties of the spin-s operator from the fields of the $\\sigma$ model. We also explore the connection of this model with Quantum Hall Fluids.
Dual pairs of gauged linear sigma models and derived equivalences of Calabi-Yau threefolds
Gerhardus, Andreas; Jockers, Hans
2017-04-01
In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N =(2 , 2) non-Abelian gauged linear sigma models. At low energies some of them flow to non-linear sigma models with Calabi-Yau target spaces, which emerge from non-Abelian strong coupling dynamics. The observed phase structure results in a non-trivial duality proposal among skew symplectic sigma models and connects non-complete intersection Calabi-Yau threefolds-that are non-birational among another-in a common quantum Kähler moduli space. As a consequence we find non-trivial identifications of spectra of topological B-branes, which from a modern algebraic geometry perspective imply derived equivalences among Calabi-Yau varieties. To further support our proposals, we calculate the two sphere partition function of skew symplectic sigma models to determine geometric invariants, which confirm the anticipated Calabi-Yau threefold phases. We show that the two sphere partition functions of a pair of dual skew symplectic sigma models agree in a non-trivial fashion. To carry out these calculations, we develop a systematic approach to study higher-dimensional Mellin-Barnes type integrals. In particular, these techniques admit the evaluation of two sphere partition functions for gauged linear sigma models with higher rank gauge groups, but are applicable in other contexts as well.
Renormalization of the Higgs sector in the triplet model
Aoki, Mayumi; Kikuchi, Mariko; Yagyu, Kei
2012-01-01
We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y=1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., $m_{H^{++}}^2-m_{H^+}^2\\simeq m_{H^+}^2-m_A^2$ and $m_A^2\\simeq m_H^2$, where the CP-even ($H$), the CP-odd ($A$) and the doubly-charged ($H^{\\pm\\pm}$) as well as the singly-charged ($H^\\pm$) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The $hhh$ coupling for the standard model-like Higgs boson ($h$) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.
Renormalization of the Higgs sector in the triplet model
Energy Technology Data Exchange (ETDEWEB)
Aoki, Mayumi [Institute for Theoretical Physics, Kanazawa University, Kanazawa 920-1192 (Japan); Kanemura, Shinya; Kikuchi, Mariko [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Yagyu, Kei, E-mail: keiyagyu@jodo.sci.u-toyama.ac.jp [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); National Central University, Physics and Center for Mathematics and Theoretical Physics, No. 300, Jhongda Rd., Jhongli, Taiwan (China)
2012-08-14
We study radiative corrections to the mass spectrum and the triple Higgs boson coupling in the model with an additional Y=1 triplet field. In this model, the vacuum expectation value for the triplet field is strongly constrained from the electroweak precision data, under which characteristic mass spectrum appear at the tree level; i.e., m{sub H{sup +}{sup +2}}-m{sub H{sup +2}} Asymptotically-Equal-To m{sub H{sup +2}}-m{sub A}{sup 2} and m{sub A}{sup 2} Asymptotically-Equal-To m{sub H}{sup 2}, where the CP-even (H), the CP-odd (A) and the doubly-charged (H{sup {+-}{+-}}) as well as the singly-charged (H{sup {+-}}) Higgs bosons are the triplet-like. We evaluate how the tree-level formulae are modified at the one-loop level. The hhh coupling for the standard model-like Higgs boson (h) is also calculated at the one-loop level. One-loop corrections to these quantities can be large enough for identification of the model by future precision data at the LHC or the International Linear Collider.
Functional renormalization group study of an 8-band model for the iron arsenides
Honerkamp, Carsten; Lichtenstein, Julian; Maier, Stefan A.; Platt, Christian; Thomale, Ronny; Andersen, Ole Krogh; Boeri, Lilia
2014-03-01
We investigate the superconducting pairing instabilities of eight-band models for 1111 iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.
Functional renormalization group study of an eight-band model for the iron arsenides
Lichtenstein, J.; Maier, S. A.; Honerkamp, C.; Platt, C.; Thomale, R.; Andersen, O. K.; Boeri, L.
2014-06-01
We investigate the superconducting pairing instabilities of eight-band models for the iron arsenides. Using a functional renormalization group treatment, we determine how the critical energy scale for superconductivity depends on the electronic band structure. Most importantly, if we vary the parameters from values corresponding to LaFeAsO to SmFeAsO, the pairing scale is strongly enhanced, in accordance with the experimental observation. We analyze the reasons for this trend and compare the results of the eight-band approach to those found using five-band models.
Renormalization of supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Pierce, D.M.
1998-06-01
The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M{sub W} and sin{sup 2}{theta}{sup eff}. He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses.
Networks as Renormalized Models for Emergent Behavior in Physical Systems
Paczuski, M
2005-01-01
Networks are paradigms for describing complex biological, social and technological systems. Here I argue that networks provide a coherent framework to construct coarse-grained models for many different physical systems. To elucidate these ideas, I discuss two long-standing problems. The first concerns the structure and dynamics of magnetic fields in the solar corona, as exemplified by sunspots that startled Galileo almost 400 years ago. We discovered that the magnetic structure of the corona embodies a scale free network, with spots at all scales. A network model representing the three-dimensional geometry of magnetic fields, where links rewire and nodes merge when they collide in space, gives quantitative agreement with available data, and suggests new measurements. Seismicity is addressed in terms of relations between events without imposing space-time windows. A metric estimates the correlation between any two earthquakes. Linking strongly correlated pairs, and ignoring pairs with weak correlation organize...
A sigma model field theoretic realization of Hitchin's generalized complex geometry
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V. Irnerio 46, I-40126 Bologna (Italy); I.N.F.N., sezione di Bologna (Italy)]. E-mail: zucchinir@bo.infn.it
2004-11-01
We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin-Vilkovisky classical master equation. Further, the (twisted) classical Batalin-Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology. (author)
A sigma model field theoretic realization of Hitchin's generalized complex geometry
Zucchini, R
2004-01-01
We present a sigma model field theoretic realization of Hitchin's generalized complex geometry, which recently has been shown to be relevant in compactifications of superstring theory with fluxes. Hitchin sigma model is closely related to the well known Poisson sigma model, of which it has the same field content. The construction shows a remarkable correspondence between the (twisted) integrability conditions of generalized almost complex structures and the restrictions on target space geometry implied by the Batalin--Vilkovisky classical master equation. Further, the (twisted) classical Batalin--Vilkovisky cohomology is related non trivially to a generalized Dolbeault cohomology.
Branco, N S; de Sousa, J Ricardo; Ghosh, Angsula
2008-03-01
Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.
The renormalization; La normalisation
Energy Technology Data Exchange (ETDEWEB)
Rivasseau, V. [Paris-6 Univ., Lab. de Physique Theorique, 91 - Orsay (France); Gallavotti, G. [Universita di Roma, La Sapienza, Fisica, Roma (Italy); Zinn-Justin, J. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique Theorique, 91- Gif sur Yvette (France); Connes, A. [College de France, 75 - Paris (France)]|[Institut des Hautes Etudes Scientifiques - I.H.E.S., 91 - Bures sur Yvette (France); Knecht, M. [Centre de Physique Theorique, CNRS-Luminy, 13 - Marseille (France); Mansoulie, B. [CEA Saclay, Dept. d' Astrophysique, de Physique des Particules, de Physique Nucleaire et de l' Instrumentation Associee, Serv. de Physique des Particules, 91- Gif sur Yvette (France)
2002-07-01
This document gathers 6 articles. In the first article the author reviews the theory of perturbative renormalization, discusses its limitations and gives a brief introduction to the powerful point of view of the renormalization group, which is necessary to go beyond perturbation theory and to define renormalization in a constructive way. The second article is dedicated to renormalization group methods by illustrating them with examples. The third article describes the implementation of renormalization ideas in quantum field theory. The mathematical aspects of renormalization are given in the fourth article where the link between renormalization and the Riemann-Hilbert problem is highlighted. The fifth article gives an overview of the main features of the theoretical calculations that have been done in order to obtain accurate predictions for the anomalous magnetic moments of the electron and of the muon within the standard model. The challenge is to make theory match the unprecedented accuracy of the last experimental measurements. The last article presents how ''physics beyond the standard model'' will be revealed at the large hadron collider (LHC) at CERN. This accelerator will be the first to explore the 1 TeV energy range directly. Supersymmetry, extra-dimensions and Higgs boson will be the different challenges. It is not surprising that all theories put forward today to subtend the electro-weak breaking mechanism, predict measurable or even spectacular signals at LHC. (A.C.)
Renormalization-group studies of three model systems far from equilibrium
Georgiev, Ivan Tsvetanov
This thesis describes the development of analytical and computational techniques for systems far from equilibrium and their application to three model systems. Each of the model systems reaches a non-equilibrium steady state and exhibits one or more phase transitions. We first introduce a new position-space renormalization-group approach and illustrate its application using the one-dimensional fully asymmetric exclusion process. We have constructed a recursion relation for the relevant dynamic parameters for this model and have reproduced all of the important critical features of the model, including the exact positions of the critical point and the first and second order phase boundaries. The method yields an approximate value for the critical exponent nu which is very close to the known value. The second major part of this thesis combines information theoretic techniques for calculating the entropy and a Monte Carlo renormalization-group approach. We have used this method to study and compare infinitely driven lattice gases. This approach enables us to calculate the critical exponents associated with the correlation length nu and the order parameter beta. These results are compared to the values predicted from different field theoretic treatments of the models. In the final set of calculations, we build position-space renormalization-group recursion relations from the master equations of small clusters. By obtaining the probability distributions for these clusters numerically, we develop a mapping connecting the parameters specifying the dynamics on different length scales. The resulting flow topology in some ways mimics equilibrium features, with sinks for each phase and fixed points associated with each phase boundary. In addition, though, there are added complexities in the flows, suggesting multiple regions within the ordered phase for some values of parameters, and the presence of an extra "source" fixed point within the ordered phase. Thus, this study
Non-Perturbative Renormalization
Mastropietro, Vieri
2008-01-01
The notion of renormalization is at the core of several spectacular achievements of contemporary physics, and in the last years powerful techniques have been developed allowing to put renormalization on a firm mathematical basis. This book provides a self-consistent and accessible introduction to the sophisticated tools used in the modern theory of non-perturbative renormalization, allowing an unified and rigorous treatment of Quantum Field Theory, Statistical Physics and Condensed Matter models. In particular the first part of this book is devoted to Constructive Quantum Field Theory, providi
Symmetry-respecting real-space renormalization for the quantum Ashkin-Teller model.
O'Brien, Aroon; Bartlett, Stephen D; Doherty, Andrew C; Flammia, Steven T
2015-10-01
We use a simple real-space renormalization-group approach to investigate the critical behavior of the quantum Ashkin-Teller model, a one-dimensional quantum spin chain possessing a line of criticality along which critical exponents vary continuously. This approach, which is based on exploiting the on-site symmetry of the model, has been shown to be surprisingly accurate for predicting some aspects of the critical behavior of the quantum transverse-field Ising model. Our investigation explores this approach in more generality, in a model in which the critical behavior has a richer structure but which reduces to the simpler Ising case at a special point. We demonstrate that the correlation length critical exponent as predicted from this real-space renormalization-group approach is in broad agreement with the corresponding results from conformal field theory along the line of criticality. Near the Ising special point, the error in the estimated critical exponent from this simple method is comparable to that of numerically intensive simulations based on much more sophisticated methods, although the accuracy decreases away from the decoupled Ising model point.
Composite and elementary nature of a resonance in the sigma model
Nagahiro, Hideko
2013-01-01
We analyze the mixing nature of the low-lying scalar resonance consisting of the pipi composite and the elementary particle within the sigma model. A method to disentangle the mixing is formulated in the scattering theory with the concept of the two-level problem. We investigate the composite and elementary components of the sigma meson by changing a mixing parameter. We also study the dependence of the results on model parameters such as the cut-off value and the mass of the elementary sigma meson.
Nonperturbative renormalization group in light-front three-dimensional real scalar model
Sugihara, T; Sugihara, Takanori; Yahiro, Masanobu
1997-01-01
The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as running mass and coupling so that the mass of the ground state vanishes. The marginal ($\\phi^6$) coupling dependence of the critical line is weak.
Renormalized scattering series for frequency-domain waveform modelling of strong velocity contrasts
Jakobsen, M.; Wu, R. S.
2016-08-01
An improved description of scattering and inverse scattering processes in reflection seismology may be obtained on the basis of a scattering series solution to the Helmoltz equation, which allows one to separately model primary and multiple reflections. However, the popular scattering series of Born is of limited seismic modelling value, since it is only guaranteed to converge if the global contrast is relatively small. For frequency-domain waveform modelling of realistic contrasts, some kind of renormalization may be required. The concept of renormalization is normally associated with quantum field theory, where it is absolutely essential for the treatment of infinities in connection with observable quantities. However, the renormalization program is also highly relevant for classical systems, especially when there are interaction effects that act across different length scales. In the scattering series of De Wolf, a renormalization of the Green's functions is achieved by a split of the scattering potential operator into fore- and backscattering parts; which leads to an effective reorganization and partially re-summation of the different terms in the Born series, so that their order better reflects the physics of reflection seismology. It has been demonstrated that the leading (single return) term in the De Wolf series (DWS) gives much more accurate results than the corresponding Born approximation, especially for models with high contrasts that lead to a large accumulation of phase changes in the forward direction. However, the higher order terms in the DWS that are associated with internal multiples have not been studied numerically before. In this paper, we report from a systematic numerical investigation of the convergence properties of the DWS which is based on two new operator representations of the DWS. The first operator representation is relatively similar to the original scattering potential formulation, but more global and explicit in nature. The second
Montag, J. Lee; Family, Fereydoon; Vicsek, Tamas; Nakanishi, Hisao
1985-10-01
We propose a new phenomenological rule for the weight function in the position-space renormalization-group approach for the calculation of the fractal dimension in models of geometrical disorder in order to avoid strong corrections to scaling due to surface effects. In our scheme the radius of gyration is used as a characteristic measure of the spatial extent of the clusters. In addition, an optimization parameter is introduced. Application to diffusion-limited aggregation in two dimensions shows that our method gives good estimates even when relatively small cells are used.
Renormalization group running of fermion observables in an extended non-supersymmetric SO(10) model
Meloni, Davide; Ohlsson, Tommy; Riad, Stella
2017-03-01
We investigate the renormalization group evolution of fermion masses, mixings and quartic scalar Higgs self-couplings in an extended non-supersymmetric SO(10) model, where the Higgs sector contains the 10 H, 120 H, and 126 H representations. The group SO(10) is spontaneously broken at the GUT scale to the Pati-Salam group and subsequently to the Standard Model (SM) at an intermediate scale M I. We explicitly take into account the effects of the change of gauge groups in the evolution. In particular, we derive the renormalization group equations for the different Yukawa couplings. We find that the computed physical fermion observables can be successfully matched to the experimental measured values at the electroweak scale. Using the same Yukawa couplings at the GUT scale, the measured values of the fermion observables cannot be reproduced with a SM-like evolution, leading to differences in the numerical values up to around 80%. Furthermore, a similar evolution can be performed for a minimal SO(10) model, where the Higgs sector consists of the 10 H and 126 H representations only, showing an equally good potential to describe the low-energy fermion observables. Finally, for both the extended and the minimal SO(10) models, we present predictions for the three Dirac and Majorana CP-violating phases as well as three effective neutrino mass parameters.
WIEDEMANN, A; MULLERKIRSTEN, HJW
1993-01-01
Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this
Extended sigma-model in nontrivially deformed field-antifield formalism
Batalin, Igor A
2015-01-01
We propose an action for the extended sigma - models in the most general setting of the kinetic term allowed in the nontrivially deformed field - antifield formalism. We show that the classical motion equations do naturally take their desired canonical form.
On the geometry of classically integrable two-dimensional non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Mohammedi, N., E-mail: nouri@lmpt.univ-tours.f [Laboratoire de Mathematiques et Physique Theorique (CNRS - UMR 6083), Universite Francois Rabelais de Tours, Faculte des Sciences et Techniques, Parc de Grandmont, F-37200 Tours (France)
2010-11-11
A master equation expressing the zero curvature representation of the equations of motion of a two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. Special attention is paid to those representations possessing a spectral parameter. Furthermore, a closer connection between integrability and T-duality transformations is emphasised. Finally, new integrable non-linear sigma models are found and all their corresponding Lax pairs depend on a spectral parameter.
On Tachyons in Generic Orbifolds of $\\BC^r$ and Gauged Linear Sigma Models
Sarkar, Tapobrata
2006-01-01
We study some aspects of Gauged Linear Sigma Models corresponding to orbifold singularities of the form $\\BC^r/\\Gamma$, for $r=2,3$ and $\\Gamma = \\BZ_n$ and $\\BZ_n\\times \\BZ_m$. These orbifolds might be tachyonic in general. We compute expressions for the multi parameter sigma model Lagrangians for these orbifolds, in terms of their toric geometry data. Using this, we analyze some aspects of the phases of generic orbifolds of $\\BC^r$.
The gauging of two-dimensional bosonic sigma models on world-sheets with defects
Gawedzki, Krzysztof; Waldorf, Konrad
2013-01-01
We extend our analysis of the gauging of rigid symmetries in bosonic two-dimensional sigma models with Wess-Zumino terms in the action to the case of world-sheets with defects. A structure that permits a non-anomalous coupling of such sigma models to world-sheet gauge fields of arbitrary topology is analysed, together with obstructions to its existence, and the classification of its inequivalent choices.
Bruns, Peter C
2016-01-01
We give some estimates for the light-quark mass dependence of the pole position of the sigma ($f_{0}(500)$) resonance in the complex energy plane, with the help of a chiral Lagrangian for the resonance field and some input from hadronic models constrained by Chiral Perturbation Theory and elastic unitarity. We also speculate on the fate of the sigma resonance when the quark masses become unphysically large.
Topological self-dual configurations in a Lorentz-violating gauged O(3) sigma model
Casana, R; Ferreira, M M
2015-01-01
We have studied the existence of topological BPS or self-dual configurations in a Lorentz-violating gauged O(3) nonlinear sigma model, where CPT-even Lorentz-violating (LV) terms were introduced in both the gauge and {\\sigma}-field sectors. Such as it happens in the usual gauged {\\sigma}-model, purely magnetic self-dual configurations are allowed, maintaining some qualitative features of the standard ones. In a more involved configuration, Lorentz-violation provides new self-dual magnetic solutions carrying electric field but null total electric charge. In both cases, the total energy of the self-dual configurations turns out proportional to the topological charge of the model and to the LV parameters introduced in the {\\sigma}-sector. It is shown that the LV terms yield magnetic flux reversion as well.
Nuclear matter properties in the relativistic mean field model with $\\sigma-\\omega$ coupling
Chung, K C; Santiago, A J; Zhang, J W
2001-01-01
The possibility of extending the linear sigma-omega model by introducing a sigma-omega coupling phenomenologically is explored. It is shown that, in contrast to the usual Walecka model, not only the effective nucleon mass M* but also the effective sigma meson mass m*_sigma and the effective omega meson mass m*_omega are nucleon density dependent. When the model parameters are fitted to the nuclear saturation point (the nuclear radius constant r_0=1.14fm and volume energy a_1=16.0MeV) as well as to the effective nucleon mass M*=0.85M, the model yields m*_sigma=1.09m_sigma and m*_omega=0.90m_omega at the saturation point, and the nuclear incompressibility K_0=501MeV. The lowest value of K_0 given by this model by adjusting the model parameters is around 227MeV.
SIX SIGMA OPTIMIZATION IN SHEET METAL FORMING BASED ON DUAL RESPONSE SURFACE MODEL
Institute of Scientific and Technical Information of China (English)
LI Yuqiang; CUI Zhenshan; ZHANG Dongjuan; RUAN Xueyu; CHEN Jun
2006-01-01
Iterations in optimization and numerical simulation for the sheet metal forming process may lead to extensive computation. In addition, uncertainties in materials or processing parameters may have great influence on the design quality. A six sigma optimization method is proposed, by combining the dual response surface method (DRSM) and six sigma philosophy, to save computation cost and improve reliability and robustness of parts. Using this method, statistical technology,including the design of experiment and analysis of variance, approximate model and six sigma philosophy are integrated together to achieve improved quality. Two sheet metal forming processes are provided as examples to illustrate the proposed method.
Real-space renormalization group for the transverse-field Ising model in two and three dimensions.
Miyazaki, Ryoji; Nishimori, Hidetoshi; Ortiz, Gerardo
2011-05-01
The two- and three-dimensional transverse-field Ising models with ferromagnetic exchange interactions are analyzed by means of the real-space renormalization-group method. The basic strategy is a generalization of a method developed for the one-dimensional case, which exploits the exact invariance of the model under renormalization and is known to give the exact values of the critical point and critical exponent ν. The resulting values of the critical exponent ν in two and three dimensions are in good agreement with those for the classical Ising model in three and four dimensions. To the best of our knowledge, this is the first example in which a real-space renormalization group on (2+1)- and (3+1)-dimensional Bravais lattices yields accurate estimates of the critical exponents.
On Renormalizing Viscous Fluids as Models for Large Scale Structure Formation
Führer, Florian
2015-01-01
We consider renormalization of the Adhesion Model for cosmic structure formation. This is a simple model that shares many relevant features of recent approaches which add effective viscosity and noise terms to the fluid equations of Cold Dark Matter, offering itself as a pedagogical playground to study the removal of the cutoff dependence from loop integrals. We show in this context that if the viscosity and noise terms are treated as perturbative corrections to the standard eulerian perturbation theory, as is done for example in the Effective Field Theory of Large Scale Structure (EFToLSS) approach, they are necessarily non-local in time. To ensure Galilean Invariance higher order vertices related to the viscosity and the noise must be added. We explicitly show at one-loop that these terms act as counter terms for vertex diagrams, while the Ward Identities ensure that the non-local theory can be renormalized consistently. A local-in-time theory is renormalizable if the viscosity is included in the linear pro...
Renormalization group: New relations between the parameters of the Standard Model
Juárez W., S. Rebeca; Kielanowski, Piotr; Mora, Gerardo; Bohm, Arno
2017-09-01
We analyze the renormalization group equations for the Standard Model at the one and two loops levels. At one loop level we find an exact constant of evolution built from the product of the quark masses and the gauge couplings g1 and g3 of the U (1) and SU (3) groups. For leptons at one loop level we find that the ratio of the charged lepton mass and the power of g1 varies ≃ 4 ×10-5 in the whole energy range. At the two loop level we have found two relations between the quark masses and the gauge couplings that vary ≃ 4% and ≃ 1%, respectively. For leptons at the two loop level we have derived a relation between the charged lepton mass and the gauge couplings g1 and g2 that varies ≃ 0.1%. This analysis significantly simplifies the picture of the renormalization group evolution of the Standard Model and establishes new important relations between its parameters. There is also included a discussion of the gauge invariance of our relations and its possible relation to the reduction of couplings method.
Renormalization group: New relations between the parameters of the Standard Model
Directory of Open Access Journals (Sweden)
S. Rebeca Juárez W.
2017-09-01
Full Text Available We analyze the renormalization group equations for the Standard Model at the one and two loops levels. At one loop level we find an exact constant of evolution built from the product of the quark masses and the gauge couplings g1 and g3 of the U(1 and SU(3 groups. For leptons at one loop level we find that the ratio of the charged lepton mass and the power of g1 varies ≃4×10−5 in the whole energy range. At the two loop level we have found two relations between the quark masses and the gauge couplings that vary ≃4% and ≃1%, respectively. For leptons at the two loop level we have derived a relation between the charged lepton mass and the gauge couplings g1 and g2 that varies ≃0.1%. This analysis significantly simplifies the picture of the renormalization group evolution of the Standard Model and establishes new important relations between its parameters. There is also included a discussion of the gauge invariance of our relations and its possible relation to the reduction of couplings method.
Saichev, A
2005-01-01
Several recent works point out that the crowd of small unobservable earthquakes (with magnitudes below the detection threshold $m_d$) may play a significant and perhaps dominant role in triggering future seismicity. Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to investigate how the statistical properties of observable earthquakes differ from the statistics of all events. The ETAS (epidemic-type aftershock sequence) model assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from the cascade of aftershocks of each past earthquake. The triggering efficiency of earthquakes is assumed to vanish below a lower magnitude limit $m_0$, in order to ensure the convergence of the theory and may reflect the physics of state-and-velocity frictional rupture. We show that, to a good approximation, the ETAS model is renormalized onto itself under what amounts to a decimation procedure $m_...
Minimalistic real-space renormalization of Ising and Potts Models in two dimensions
Directory of Open Access Journals (Sweden)
Gary eWillis
2015-06-01
Full Text Available We introduce and discuss a real-space renormalization group (RSRG procedure on very small lattices, which in principle does not require any of the usual approximations, e.g. a cut-off in the expansion of the Hamiltonian in powers of the field. The procedure is carried out numerically on very small lattices (4x4 to 2x2 and implemented for the Ising Model and the q=3,4,5 Potts Models. Nevertheless, the resulting estimates of the correlation length exponent and the magnetization exponent are typically within 3% to 7% of the exact values. The 4-state Potts Model generates a third magnetic exponent which seems to be unknown in the literature. A number of questions about the meaning of certain exponents and the procedure itself arise from its use of symmetry principles and its application to the q=5 Potts Model.
Johnson, D. R.; Uccellini, L. W.
1983-01-01
In connection with the employment of the sigma coordinates introduced by Phillips (1957), problems can arise regarding an accurate finite-difference computation of the pressure gradient force. Over steeply sloped terrain, the calculation of the sigma-coordinate pressure gradient force involves computing the difference between two large terms of opposite sign which results in large truncation error. To reduce the truncation error, several finite-difference methods have been designed and implemented. The present investigation has the objective to provide another method of computing the sigma-coordinate pressure gradient force. Phillips' method is applied for the elimination of a hydrostatic component to a flux formulation. The new technique is compared with four other methods for computing the pressure gradient force. The work is motivated by the desire to use an isentropic and sigma-coordinate hybrid model for experiments designed to study flow near mountainous terrain.
Renormalized Unruh-DeWitt Particle Detector Models for Boson and Fermion Fields
Hümmer, Daniel; Kempf, Achim
2016-01-01
Since quantum field theories do not possess proper position observables, Unruh-DeWitt detector models serve as a key theoretical tool for extracting localized spatio-temporal information from quantum fields. Most studies have been limited, however, to Unruh-DeWitt (UDW) detectors that are coupled linearly to a scalar bosonic field. Here, we investigate UDW detector models that probe fermionic as well as bosonic fields through both linear and quadratic couplings. In particular, we present a renormalization method that cures persistent divergencies of prior models. We then show how perturbative calculations with UDW detectors can be streamlined through the use of extended Feynman rules that include localized detector-field interactions.Our findings pave the way for the extension of previous studies of the Unruh and Hawking effects with UDW detectors, and provide new tools for studies in relativistic quantum information, for example, regarding relativistic quantum communication and studies of the entanglement st...
Facilitated spin models in one dimension: a real-space renormalization group study.
Whitelam, Stephen; Garrahan, Juan P
2004-10-01
We use a real-space renormalization group (RSRG) to study the low-temperature dynamics of kinetically constrained Ising chains (KCICs). We consider the cases of the Fredrickson-Andersen (FA) model, the East model, and the partially asymmetric KCIC. We show that the RSRG allows one to obtain in a unified manner the dynamical properties of these models near their zero-temperature critical points. These properties include the dynamic exponent, the growth of dynamical length scales, and the behavior of the excitation density near criticality. For the partially asymmetric chain, the RG predicts a crossover, on sufficiently large length and time scales, from East-like to FA-like behavior. Our results agree with the known results for KCICs obtained by other methods.
Bartkowiak, M.; Münger, P.; Micnas, R.
A diagrammatic technique for Hubbard's operators is employed to perform systematically the high-density expansion for the three-dimensional spinless fermion model. The molecular field theory is obtained by the zero-order renormalization of blocks. Summation of the first order diagrams is carried out in both selfconsistent and correctional way. It turns out that the charge ordering parameter, calculated self-consistently, has a jump for a certain medial temperature. We have also shown, that the Horwitz-Callen renormalization leads to the first or second order phase transition, depending on t/W and fails when this ratio is large enough. The phase diagrams of the system for the half-filled band case, derived in both unrenormalized and renormalized first order of high-density expansion are presented.
Qin, Meng; Ren, Zhong-Zhou; Zhang, Xin
2016-01-01
In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.
Institute of Scientific and Technical Information of China (English)
Ma Lei; Huang Ai-Qun; Li Jun
2011-01-01
This paper studies the normal state properties of itinerant electrons in a toy model, which is constructed according to the model for coexisting ferromagnetism and superconductivity proposed by Suhl [Suhl H 2001 Phys. Rev. Lett. 87 167007]. In this theory with ferromagnetic ordering based on localized spins, the exchange interaction J between conduction electrons and localized spin is taken as the pairing glue for s-wave superconductivity. It shows that this J term will first renormalize the normal state single conduction electron structures substantially. It finds dramatically enhanced or suppressed magnetization of itinerant electrons for positive or negative J. Singlet Cooper pairing can be ruled out due to strong spin polarisation in the J > 0 case while a narrow window for s-wave superconductivity is opened around some ferromagnetic J.
Higgs mass bounds from renormalization flow for a Higgs-top-bottom model
Energy Technology Data Exchange (ETDEWEB)
Gies, Holger; Sondenheimer, Rene [Friedrich-Schiller-Universitaet Jena, Theoretisch-Physikalisches Institut, Jena (Germany)
2015-02-01
We study a chiral Yukawa model mimicking the Higgs-top-bottom sector of the standard model. We reanalyze the conventional arguments that relate a lower bound for the Higgs mass with vacuum stability in the light of exact results for the regularized fermion determinant as well as in the framework of the functional renormalization group. In both cases, we find no indication for vacuum instability nor meta-stability induced by top fluctuations if the cutoff is kept finite but arbitrary. A lower bound for the Higgs mass arises for the class of standard bare potentials of φ{sup 4} type from the requirement of a well-defined functional integral (i.e., stability of the bare potential). This consistency bound can, however, be relaxed considerably by more general forms of the bare potential without necessarily introducing new metastable minima. (orig.)
Renormalization of fermion mixing
Energy Technology Data Exchange (ETDEWEB)
Schiopu, R.
2007-05-11
Precision measurements of phenomena related to fermion mixing require the inclusion of higher order corrections in the calculation of corresponding theoretical predictions. For this, a complete renormalization scheme for models that allow for fermion mixing is highly required. The correct treatment of unstable particles makes this task difficult and yet, no satisfactory and general solution can be found in the literature. In the present work, we study the renormalization of the fermion Lagrange density with Dirac and Majorana particles in models that involve mixing. The first part of the thesis provides a general renormalization prescription for the Lagrangian, while the second one is an application to specific models. In a general framework, using the on-shell renormalization scheme, we identify the physical mass and the decay width of a fermion from its full propagator. The so-called wave function renormalization constants are determined such that the subtracted propagator is diagonal on-shell. As a consequence of absorptive parts in the self-energy, the constants that are supposed to renormalize the incoming fermion and the outgoing antifermion are different from the ones that should renormalize the outgoing fermion and the incoming antifermion and not related by hermiticity, as desired. Instead of defining field renormalization constants identical to the wave function renormalization ones, we differentiate the two by a set of finite constants. Using the additional freedom offered by this finite difference, we investigate the possibility of defining field renormalization constants related by hermiticity. We show that for Dirac fermions, unless the model has very special features, the hermiticity condition leads to ill-defined matrix elements due to self-energy corrections of external legs. In the case of Majorana fermions, the constraints for the model are less restrictive. Here one might have a better chance to define field renormalization constants related by
Numerical renormalization group studies of the partially brogen SU(3) Kondo model
Energy Technology Data Exchange (ETDEWEB)
Fuh Chuo, Evaristus
2013-04-15
The two-channel Kondo (2CK) effect with its exotic ground state properties has remained difficult to realize in physical systems. At low energies, a quantum impurity with orbital degree of freedom, like a proton bound in an interstitial lattice space, comprises a 3-level system with a unique ground state and (at least) doubly degenerate rotational excitations with excitation energy {Delta}{sub 0}. When immersed in a metal, electronic angular momentum scattering induces transitions between any two of these levels (couplings J), while the electron spin is conserved. We show by extensive numerical renormalization group (NRG) calculations that without fi ne-tuning of parameters this system exhibits a 2CK fixed point, due to Kondo correlations in the excited-state doublet whose degeneracy is stabilized by the host lattice parity, while the channel symmetry (electron spin) is guaranteed by time reversal symmetry. We find a pronounced plateau in the entropy at S(T{sub K}
Sigma terms of octet baryons in the extended chiral constituent quark model
An, C S
2014-01-01
{\\bf Background:} Quantitative insight into the respective roles played by the valence flavors and the sea quark-antiquark pairs in the baryons is crucial in deepening our comprehension of nonperturbative QCD. {\\bf Purpose:} Study the meson-baryon $\\sigma$-terms for the ground-state octet baryons $B \\equiv N,~\\Lambda,~\\Sigma,~\\Xi$. {\\bf Methods:} Within an extended chiral constituent quark model, we investigate contributions from all possible five-quark components to the $\\sigma$-terms. The probabilities of the quark-antiquark components in the baryons wave functions are calculated by taking the baryons to be admixtures of three- and five-quark components, with the relevant transitions handled {\\it via} the $^{3}P_{0}$ mechanism. {\\bf Results:} Predictions are obtained by using input parameters taken from the literature. Numerical results for the meson-nucleon and the dimensionless ${\\sigma}$-terms, $\\bar {\\sigma}_{Bl}$ and $\\bar {\\sigma}_{Bs}$, are reported. {\\bf Conclusions:} Our results turn out to be, in ...
Numerical renormalization group for the bosonic single-impurity Anderson model: Dynamics
Lee, Hyun-Jung; Byczuk, Krzysztof; Bulla, Ralf
2010-08-01
The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization-group calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
Wang, Chumin; Salazar, Fernando; Sánchez, Vicenta
2008-12-01
Based on the Kubo-Greenwood formula, the transport of electrons and phonons in nanowires is studied by means of a real-space renormalization plus convolution method. This method has the advantage of being efficient, without introducing additional approximations and capable to analyze nanowires of a wide range of lengths even with defects. The Born and tight-binding models are used to investigate the lattice thermal and electrical conductivities, respectively. The results show a quantized electrical dc conductance, which is attenuated when an oscillating electric field is applied. Effects of single and multiple planar defects, such as a quasi-periodic modulation, on the conductance of nanowires are also investigated. For the low temperature region, the lattice thermal conductance reveals a power-law temperature dependence, in agreement with experimental data.
Renormalization group analysis of reduced magnetohydrodynamics with application to subgrid modeling
Longcope, D. W.; Sudan, R. N.
1991-01-01
The technique for obtaining a subgrid model for Navier-Stokes turbulence, based on renormalization group analysis (RNG), is extended to the reduced magnetohydrodynamic (RMND) equations. It is shown that a RNG treatment of the Alfven turbulence supported by the RMHD equations leads to effective values of the viscosity and resistivity at large scales, k yields 0, dependent on the amplitude of turbulence. The effective viscosity and resistivity become independent of the molecular quantities when the RNG analysis is augmented by the Kolmogorov argument for energy cascade. A self-contained system of equations is derived for the range of scales, k = 0-K, where K = pi/Delta is the maximum wave number for a grid size Delta. Differential operators, whose coefficients depend upon the amplitudes of the large-scale quantities, represent in this system the resistive and viscous dissipation.
Quinto, A. G.; Ferrari, A. F.; Lehum, A. C.
2016-06-01
In this work, we investigate the consequences of the Renormalization Group Equation (RGE) in the determination of the effective superpotential and the study of Dynamical Symmetry Breaking (DSB) in an N = 1 supersymmetric theory including an Abelian Chern-Simons superfield coupled to N scalar superfields in (2 + 1) dimensional spacetime. The classical Lagrangian presents scale invariance, which is broken by radiative corrections to the effective superpotential. We calculate the effective superpotential up to two-loops by using the RGE and the beta functions and anomalous dimensions known in the literature. We then show how the RGE can be used to improve this calculation, by summing up properly defined series of leading logs (LL), next-to-leading logs (NLL) contributions, and so on... We conclude that even if the RGE improvement procedure can indeed be applied in a supersymmetric model, the effects of the consideration of the RGE are not so dramatic as it happens in the non-supersymmetric case.
BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term
Huang, Yong-Chang; Lee, Xi-Guo
2006-01-01
We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.
Exact solutions of SO(3) non-linear sigma model in a conic space background
Bezerra, V B; Romero, C
2005-01-01
We consider a nonlinear sigma model coupled to the metric of a conic space. We obtain restrictions for a nonlinear sigma model to be a source of the conic space. We then study nonlinear sigma model in the conic space background. We find coordinate transformations which reduce the chiral fields equations in the conic space background to field equations in Minkowski spacetime. This enables us to apply the same methods for obtaining exact solutions in Minkowski spacetime to the case of a conic spacetime. In the case the solutions depend on two spatial coordinates we employ Ivanov's geometrical ansatz. We give a general analysis and also present classes of solutions in which there is dependence on three and four coordinates. We discuss with special attention the intermediate instanton and meron solutions and their analogous in the conic space. We find differences in the total actions and topological charges of these solutions and discuss the role of the deficit angle.
Ikeda, Noriaki; Xu, Xiaomeng
2014-11-01
Consistent boundary conditions for Alexandrov-Kontsevich-Schwartz-Zaboronsky (AKSZ) sigma models and the corresponding boundary theories are analyzed. As their mathematical structures, we introduce a generalization of differential graded symplectic manifolds, called twisted QP manifolds, in terms of graded symplectic geometry, canonical functions, and QP pairs. We generalize the AKSZ construction of topological sigma models to sigma models with Wess-Zumino terms and show that all the twisted Poisson-like structures known in the literature can actually be naturally realized as boundary conditions for AKSZ sigma models.
Energy Technology Data Exchange (ETDEWEB)
Kuchinskii, E. Z.; Nekrasov, I. A., E-mail: nekrasov@iep.uran.ru; Pavlov, N. S. [Russian Academy of Sciences, Institute of Electrophysics, Ural Branch (Russian Federation)
2013-08-15
We propose a generalization of the LDA + DMFT + {Sigma}{sub k} approach to the multiband case, in which correlated and uncorrelated states are present in the model simultaneously. Using the multiband version of the LDA + DMFT + {Sigma}{sub k} approach, we calculate the density of states and spectral functions for the Emery model in a wide energy interval around the Fermi level. We also obtain the Fermi surfaces for the electron-doped high-temperature superconductor Nd{sub 2-x}Ce{sub x}CuO{sub 4} in the pseudogap phase. The self-energy part {Sigma}{sub k} introduced additionally to take into account pseudogap fluctuations describes the nonlocal interaction of correlated electrons with collective Heisenberg short-range spin fluctuations. To solve the effective impurity model, the numerical renorm-group (NRG) method is used for the DMFT equations. Good qualitative agreement of the Fermi surfaces calculated using the LDA + DMFT + {Sigma}{sub k} approach and experimental angle-resolved photoemission spectroscopic data is attained. The stability of the dielectric solution with charge transfer in the Emery model with correction for double counting is analyzed in the Appendix.
SIGMA: A Knowledge-Based Simulation Tool Applied to Ecosystem Modeling
Dungan, Jennifer L.; Keller, Richard; Lawless, James G. (Technical Monitor)
1994-01-01
The need for better technology to facilitate building, sharing and reusing models is generally recognized within the ecosystem modeling community. The Scientists' Intelligent Graphical Modelling Assistant (SIGMA) creates an environment for model building, sharing and reuse which provides an alternative to more conventional approaches which too often yield poorly documented, awkwardly structured model code. The SIGMA interface presents the user a list of model quantities which can be selected for computation. Equations to calculate the model quantities may be chosen from an existing library of ecosystem modeling equations, or built using a specialized equation editor. Inputs for dim equations may be supplied by data or by calculation from other equations. Each variable and equation is expressed using ecological terminology and scientific units, and is documented with explanatory descriptions and optional literature citations. Automatic scientific unit conversion is supported and only physically-consistent equations are accepted by the system. The system uses knowledge-based semantic conditions to decide which equations in its library make sense to apply in a given situation, and supplies these to the user for selection. "Me equations and variables are graphically represented as a flow diagram which provides a complete summary of the model. Forest-BGC, a stand-level model that simulates photosynthesis and evapo-transpiration for conifer canopies, was originally implemented in Fortran and subsequenty re-implemented using SIGMA. The SIGMA version reproduces daily results and also provides a knowledge base which greatly facilitates inspection, modification and extension of Forest-BGC.
3D loop models and the CP(n-1) sigma model.
Nahum, Adam; Chalker, J T; Serna, P; Ortuño, M; Somoza, A M
2011-09-09
Many statistical mechanics problems can be framed in terms of random curves; we consider a class of three-dimensional loop models that are prototypes for such ensembles. The models show transitions between phases with infinite loops and short-loop phases. We map them to CP(n-1) sigma models, where n is the loop fugacity. Using Monte Carlo simulations, we find continuous transitions for n=1, 2, 3, and first order transitions for n≥5. The results are relevant to line defects in random media, as well as to Anderson localization and (2+1)-dimensional quantum magnets.
Static solution of the general relativistic nonlinear $\\sigma$model equation
Lee, C H; Lee, H K; Lee, Chul H; Kim, Joon Ha; Lee, Hyun Kyu
1994-01-01
The nonlinear \\sigma-model is considered to be useful in describing hadrons (Skyrmions) in low energy hadron physics and the approximate behavior of the global texture. Here we investigate the properties of the static solution of the nonlinear \\sigma-model equation coupled with gravity. As in the case where gravity is ignored, there is still no scale parameter that determines the size of the static solution and the winding number of the solution is 1/2. The geometry of the spatial hyperspace in the asymptotic region of large r is explicitly shown to be that of a flat space with some missing solid angle.
Batalin, Igor A.; Lavrov, Peter M.
2017-04-01
For topological sigma models, we propose that their local Lagrangian density is allowed to depend non-linearly on the de Rham's "velocities" DZA. Then, by differentiating the Lagrangian density with respect to the latter de Rham's "velocities", we define a "dynamical" anti-symplectic potential, in terms of which a "dynamical" anti-symplectic metric is defined, as well. We define the local and the functional antibracket via the dynamical anti-symplectic metric. Finally, we show that the generalized action of the sigma model satisfies the functional master equation, as required.
On tachyons in generic orbifolds of C{sup r} and gauged linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Tapobrata [Department of Physics, Indian Institute of Technology, Kanpur 208016 (India)
2007-02-15
We study some aspects of Gauged Linear Sigma Models corresponding to orbifold singularities of the form C{sup r}/{gamma}, for r = 2,3 and {gamma} = Z{sub n} and Z{sub n} x Z{sub m}. These orbifolds might be tachyonic in general. We compute expressions for the multi parameter sigma model Lagrangians for these orbifolds, in terms of their toric geometry data. Using this, we analyze some aspects of the phases of generic orbifolds of C{sup r}.
Off-shell superconformal nonlinear sigma-models in three dimensions
Kuzenko, Sergei M; Tartaglino-Mazzucchelli, Gabriele; von Unge, Rikard
2010-01-01
We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.
Sigma models for bundles on Calabi-Yau: a proposal for matrix string compactifications
Hofman, C.; Park, J.-S.
2001-01-01
W e describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Y au 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped around the Calabi-Yau. We propose that this model can be us
C(M)LESS-THAN-1 STRING THEORY AS A CONSTRAINED TOPOLOGICAL SIGMA-MODEL
LLATAS, PM; ROY, S
1995-01-01
It has been argued by Ishikawa and Kato that by making use of a specific bosonization, c(M) = 1 string theory can be regarded as a constrained topological sigma model. We generalize their construction for any (p,q) minimal model coupled to two dimensional (2d) gravity and show that the energy-moment
The classical r-matrix method for nonlinear sigma-model
Sevostyanov, Alexey
1995-01-01
The canonical Poisson structure of nonlinear sigma-model is presented as a Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson structure of this model is determined by some `hidden singularities' of the Lax matrix.
Directory of Open Access Journals (Sweden)
Adriana Barbosa Santos
2008-04-01
Full Text Available Este artigo apresenta o modelo de referência para estruturar o Seis Sigma, o qual é resultante da incorporação de teorias que contribuem para aumentar o potencial estratégico do Seis Sigma no sentido de incrementar o desempenho organizacional. Em sua proposta, o modelo de referência engloba um direcionamento sobre certos requisitos primordiais para o sucesso do programa Seis Sigma. A base teórica de sustentação do modelo de referência foi construída a partir de estudos sobre a influência dos seguintes fatores: orientação estratégica e alinhamento estratégico; medição e gerenciamento do desempenho organizacional; uso de estatística (pensamento estatístico; capacitação/especialização de pessoas; implementação e gerenciamento de projetos; e uso de tecnologia de informação. Complementando a proposição do modelo, o artigo traz evidências empíricas acerca da contribuição dos fatores identificados na formulação do modelo de referência, expondo resultados decorrentes de estudos de caso realizados em quatro subsidiárias brasileiras de multinacionais de grande porte. A análise dos dados forneceu evidências positivas de que os fatores mencionados influenciam de forma efetiva o sucesso e a consolidação do Seis Sigma nas empresas estudadas.This paper introduces the reference model to structure Six Sigma. This model is a result of theory incorporation that contributes to increase the strategic power of Six Sigma for improving businesses performance. Reference model proposal points out certain primordial requirements for de Six Sigma program success. The theoretical basis to sustain the reference model was supported in studies about the influence of critical factors such as: strategic orientation and strategic alignment; business performance measurement; statistical approach (statistical thinking; people training; project implementation; and information technology use. Complementing the model proposition, this paper
Scaling symmetry, renormalization, and time series modeling: the case of financial assets dynamics.
Zamparo, Marco; Baldovin, Fulvio; Caraglio, Michele; Stella, Attilio L
2013-12-01
We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling with time of the probability density of their aggregates. In its simplest version the model is the product of an endogenous autoregressive component and a random rescaling factor designed to embody also exogenous influences. Mathematical properties like increments' stationarity and ergodicity can be proven. Thanks to the relatively low number of parameters, model calibration can be conveniently based on a method of moments, as exemplified in the case of historical data of the S&P500 index. The calibrated model accounts very well for many stylized facts, like volatility clustering, power-law decay of the volatility autocorrelation function, and multiscaling with time of the aggregated return distribution. In agreement with empirical evidence in finance, the dynamics is not invariant under time reversal, and, with suitable generalizations, skewness of the return distribution and leverage effects can be included. The analytical tractability of the model opens interesting perspectives for applications, for instance, in terms of obtaining closed formulas for derivative pricing. Further important features are the possibility of making contact, in certain limits, with autoregressive models widely used in finance and the possibility of partially resolving the long- and short-memory components of the volatility, with consistent results when applied to historical series.
Lavrov, P. M.; Shapiro, I. L.
2012-09-01
We consider the renormalization of general gauge theories on curved space-time background, with the main assumption being the existence of a gauge-invariant and diffeomorphism invariant regularization. Using the Batalin-Vilkovisky (BV) formalism one can show that the theory possesses gauge invariant and diffeomorphism invariant renormalizability at quantum level, up to an arbitrary order of the loop expansion.
Renormalization-group theory for cooling first-order phase transitions in Potts models.
Liang, Ning; Zhong, Fan
2017-03-01
We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q-state Potts model for q>10/3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.
Renormalization-group theory for cooling first-order phase transitions in Potts models
Liang, Ning; Zhong, Fan
2017-03-01
We develop a dynamic field-theoretic renormalization-group (RG) theory for cooling first-order phase transitions in the Potts model. It is suggested that the well-known imaginary fixed points of the q -state Potts model for q >10 /3 in the RG theory are the origin of the dynamic scaling found recently from numerical simulations, apart from logarithmic corrections. This indicates that the real and imaginary fixed points of the Potts model are both physical and control the scalings of the continuous and discontinuous phase transitions, respectively, of the model. Our one-loop results for the scaling exponents are already not far away from the numerical results. Further, the scaling exponents depend on q only slightly, consistent with the numerical results. Therefore, the theory is believed to provide a natural explanation of the dynamic scaling including the scaling exponents and their scaling laws for various observables in the cooling first-order phase transition of the Potts model.
Diep, H T; Kaufman, Miron
2009-09-01
We extend the model of a 2d solid to include a line of defects. Neighboring atoms on the defect line are connected by springs of different strength and different cohesive energy with respect to the rest of the system. Using the Migdal-Kadanoff renormalization group we show that the elastic energy is an irrelevant field at the bulk critical point. For zero elastic energy this model reduces to the Potts model. By using Monte Carlo simulations of the three- and four-state Potts model on a square lattice with a line of defects, we confirm the renormalization-group prediction that for a defect interaction larger than the bulk interaction the order parameter of the defect line changes discontinuously while the defect energy varies continuously as a function of temperature at the bulk critical temperature.
Local renormalization method for random systems
Gittsovich O.; Hubener R.; Rico E.; Briegel H.J.
2010-01-01
In this paper, we introduce a real-space renormalization transformation for random spin systems on 2D lattices. The general method is formulated for random systems and results from merging two well known real space renormalization techniques, namely the strong disorder renormalization technique (SDRT) and the contractor renormalization (CORE). We analyze the performance of the method on the 2D random transverse field Ising model (RTFIM).
Capillary-wave models and the effective-average-action scheme of functional renormalization group.
Jakubczyk, P
2011-08-01
We reexamine the functional renormalization-group theory of wetting transitions. As a starting point of the analysis we apply an exact equation describing renormalization group flow of the generating functional for irreducible vertex functions. We show how the standard nonlinear renormalization group theory of wetting transitions can be recovered by a very simple truncation of the exact flow equation. The derivation makes all the involved approximations transparent and demonstrates the applicability of the approach in any spatial dimension d≥2. Exploiting the nonuniqueness of the renormalization-group cutoff scheme, we find, however, that the capillary parameter ω is a scheme-dependent quantity below d=3. For d=3 the parameter ω is perfectly robust against scheme variation.
Higgs mass bounds from renormalization flow for a Higgs–top–bottom model
National Research Council Canada - National Science Library
Gies, Holger; Sondenheimer, René
2015-01-01
... framework of the functional renormalization group. In both cases, we find no indication for vacuum instability nor meta-stability induced by top fluctuations if the cutoff is kept finite but arbitrary...
Density-Matrix Renormalization Group Study of Kitaev-Heisenberg Model on a Triangular Lattice
Shinjo, Kazuya; Sota, Shigetoshi; Yunoki, Seiji; Totsuka, Keisuke; Tohyama, Takami
2016-11-01
We study the Kitaev-Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev-Heisenberg model. As suggested by previous studies, we find a 120° antiferromagnetic (AFM) phase, a Z2-vortex crystal phase, a nematic phase, a dual Z2-vortex crystal phase (the dual counterpart of the Z2-vortex crystal phase), a Z6 ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the Z6 ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev-Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.
Renormalization Group Study of the Minimal Majoronic Dark Radiation and Dark Matter Model
Chang, We-Fu
2016-01-01
We study the 1-loop renormalization group equation running in the simplest singlet Majoron model constructed by us earlier to accommodate the dark radiation and dark matter content in the universe. A comprehensive numerical study was performed to explore the whole model parameter space. A smaller effective number of neutrinos $\\triangle N_{eff}\\sim 0.05$, or a Majoron decoupling temperature higher than the charm quark mass, is preferred. We found that a heavy scalar dark matter, $\\rho$, of mass $1.5-4$ TeV is required by the stability of the scalar potential and an operational type-I see-saw mechanism for neutrino masses. A neutral scalar, $S$, of mass in the $10-100$ GeV range and its mixing with the standard model Higgs as large as $0.1$ is also predicted. The dominant decay modes are $S$ into $b\\bar{b}$ and/or $\\omega\\omega$. A sensitive search will come from rare $Z$ decays via the chain $Z\\rightarrow S+ f\\bar{f}$, where $f$ is a Standard Model fermion, followed by $S$ into a pair of Majoron and/or b-quar...
Dynamic renormalization group study of a generalized continuum model of crystalline surfaces.
Cuerno, Rodolfo; Moro, Esteban
2002-01-01
We apply the Nozières-Gallet dynamic renormalization group (RG) scheme to a continuum equilibrium model of a d-dimensional surface relaxing by linear surface tension and linear surface diffusion, and which is subject to a lattice potential favoring discrete values of the height variable. The model thus interpolates between the overdamped sine-Gordon model and a related continuum model of crystalline tensionless surfaces. The RG flow predicts the existence of an equilibrium roughening transition only for d=2 dimensional surfaces, between a flat low-temperature phase and a rough high-temperature phase in the Edwards-Wilkinson (EW) universality class. The surface is always in the flat phase for any other substrate dimensions d>2. For any value of d, the linear surface diffusion mechanism is an irrelevant perturbation of the linear surface tension mechanism, but may induce long crossovers within which the scaling properties of the linear molecular-beam epitaxy equation are observed, thus increasing the value of the sine-Gordon roughening temperature. This phenomenon originates in the nonlinear lattice potential, and is seen to occur even in the absence of a bare surface tension term. An important consequence of this is that a crystalline tensionless surface is asymptotically described at high temperatures by the EW universality class.
The O(N) linear sigma model at finite temperature beyond the Hartree approximation
Baacke, J
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking, using a Hartree-like ansatz with a classical field and variational masses. We go beyond the Hartree approximation by including the two-loop contribution, the sunset diagram, using the 2PPI expansion. We have computed numerically the effective potential at finite temperature. We find a phase transition of second order, while it is first order in the one-loop Hartree approximation. We also discuss some implications of the fact that in this order, the decay of the sigma into two pions affects the thermal diagrams.
O(N) linear sigma model beyond the Hartree approximation at finite temperature
Baacke, J; Michalski, Stefan
2003-01-01
We study the O(N) linear sigma model with spontaneous symmetry breaking at finite temperature in the framework of the two-particle point-irreducible (2PPI) effective action. We go beyond the Hartree approximation by including the two-loop contribution, i.e., the sunset diagram. A phase transition of second order is found, whereas it is of first order in the one-loop Hartree approximation. Furthermore, we show the temperature-dependence of the variational mass parameters and comment on their relation to the physical sigma and pion masses.
Landau-Lifshitz sigma-models, fermions and the AdS/CFT correspondence
Stefanski, B
2007-01-01
We define Landau-Lifshitz sigma models on general coset space $G/H$, with $H$ a maximal stability sub-group of $G$. These are non-relativistic models that have $G$-valued N\\"other charges, local $H$ invariance and are classically integrable. Using this definition, we construct the $PSU(2,2|4)/PS(U(2|2)^2)$ Landau-Lifshitz sigma-model. This sigma model describes the thermodynamic limit of the spin-chain Hamiltonian obtained from the complete one-loop dilatation operator of the N=4 super Yang-Mills (SYM) theory. In the second part of the paper, we identify a number of consistent truncations of the Type IIB Green-Schwarz action on $AdS_5\\times S^5$ whose field content consists of two real bosons and 4,8 or 16 real fermions. We show that $\\kappa$-symmetry acts trivially in these sub-sectors. In the context of the large spin limit of the AdS/CFT correspondence, we map the Lagrangians of these sub-sectors to corresponding truncations of the $PSU(2,2|4)/PS(U(2|2)^2)$ Landau-Lifshitz sigma-model.
Abu-Shady, M
2015-01-01
The chiral symmetry breaking in the presence of external magnetic field is studied in the framework of logarithmic quark-sigma model. The effective logarithmic mesonic potential is employed and is numerically solved in the mean-field approximation. We find that the chiral symmetry breaking enhances in comparison with the original sigma model. Two sets of parameterization are investigated in the present model. We find that increasing coupling constant enhances the breaking symmetry while increasing sigma mass inhibits enhancing chiral broken vacuum state. A comparison with the Numbu-Jona-Lasinio model and the Schwinger-Dyson equation is discussed. We conclude that the logarithmic sigma model enhances the magnetic catalysis in comparison with the original sigma model and other models.
Comparison of renormalization group schemes for sine-Gordon type models
Nandori, I; Sailer, K; Trombettoni, A
2009-01-01
We consider the scheme-dependence of the renormalization group (RG) flow obtained in the local potential approximation for two-dimensional periodic, sine-Gordon type field-theoric models with possible inclusion of explicit mass terms. For sine-Gordon type models showing up a Kosterlitz-Thouless-Berezinskii type phase transition the Wegner-Houghton, the Polchinski, the functional Callan-Symanzik and the effective average action RG methods give qualitatively the same result and the critical frequency (temperature) can be obtained scheme-independently from the RG equations linearized around the Gaussian fixed point. For the massive sine-Gordon model which undergoes an Ising type phase transition, the Wegner-Houghton, the functional Callan-Symanzik and the effective average action RG methods provide the same scheme-independent phase structure and value for the critical ratio, in agreement with the results of lattice methods. It is also shown that RG equations linearized around the Gaussian fixed point produce sch...
Two-Dimensional Supersymmetric Sigma Models on Almost-Product Manifolds and Non-Geometry
Stojevic, V.
2010-01-01
We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\\pm}$, and the orthogonal complements $Q_{\\pm}$, covariantly constant with respect to the two natural torsionful connections $\
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Gombor, Tamas
2015-01-01
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
Energy Technology Data Exchange (ETDEWEB)
Sato, K.; Koide, Tomoi; Maruyama, Masahiro [Tohoku Univ., Faculty of Science, Sendai, Miyagi (Japan)
1999-08-01
There are various approaches to nonequilibrium system. We use the projection operator method investigated by F. Shibata and N. Hashitsume on the linear sigma model at finite temperature and density. We derive a differential equation of the time evolution for the order parameter and pion number density in chiral phase transition. (author)
Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries
Energy Technology Data Exchange (ETDEWEB)
Gombor, Tamás [MTA Lendület Holographic QFT Group, Wigner Research Centre,H-1525 Budapest 114, P.O.B. 49 (Hungary); Institute for Theoretical Physics, Roland Eötvös University,1117 Budapest, Pázmány s. 1/A (Hungary); Palla, László [Institute for Theoretical Physics, Roland Eötvös University,1117 Budapest, Pázmány s. 1/A (Hungary)
2016-02-24
The finite volume problem of O(2N) sigma models with integrable diagonal boundaries on a finite interval is investigated. The double row transfer matrix is diagonalized by Algebraic Bethe Ansatz. The boundary Bethe Yang equations for the particle rapidities and the accompanying Bethe Ansatz equations are derived.
Extended sigma-model in nontrivially deformed field-antifield formalism
Batalin, Igor A.; Lavrov, Peter M.
2015-08-01
We propose an action for the extended sigma-models in the most general setting of the kinetic term allowed in the nontrivially deformed field-antifield formalism. We show that the classical motion equations do naturally take their desired canonical form.
The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad
2009-01-01
Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.
The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
Butter, Daniel
2011-01-01
We present a detailed study of the most general N=2 supersymmetric sigma models in four-dimensional anti-de Sitter space AdS_4 formulated in terms of N=1 chiral superfields. The target space is demonstrated to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures and necessarily leaves one of them invariant. All hyperkahler cones, that is the target spaces of N=2 superconformal sigma models, prove to possess such a vector field that belongs to the Lie algebra of an isometry group SU(2) acting by rotations on the complex structures. A unique property of the N=2 sigma models constructed is that the algebra of OSp(2|4) transformations closes off the mass shell. We uncover the underlying N=2 superfield formulation for the N=2 sigma models constructed and compute the associated N=2 supercurrent. We give a special analysis of the most general systems of self-interacting N=2 tensor multiplets in A...
T-Duality in $\\sigma$ Models with Kaluza-Klein Metric as Electric-Magnetic Duality
Jafarizadeh, M A
1999-01-01
It is shown that the T-duality in \\sigma-model with Kaluza-Klein metric, without or with a torsion term, can be interpreted as electric-magnetic duality for some of their solitonic solutions. Actually Buscher's duality transformation interchanges the topological and Noether charges.
Bose-Einstein Condensation in Linear Sigma Model at Hartree Approximation
Institute of Scientific and Technical Information of China (English)
M. Agop; SHU Song; Camelia Popa; LI Jia-Rong; Anca Harabagiu
2008-01-01
The BEC of charged pions is investigated in the framework of O(4) linear sigma model. By using Cornwall Jackiw Tomboulis formalism, we have derived the gap equations for the effective masses of the mesons at finite tempera-ture and finite isospin density. The critical temperature and phase diagram of BEC are discussed in the non-chiral limit at Hartree approximation.
Classical integrability of the O(N) nonlinear $\\sigma$ model on a half-line
Corrigan, E
1996-01-01
The classical integrability the O(N) nonlinear sigma model on a half-line is examined, and the existence of an infinity of conserved charges in involution is established for the free boundary condition. For the case N=3 other possible boundary conditions are considered briefly.
Non-linear supersymmetric {sigma}-models and their gauging in the Atiyah-Ward space-time
Energy Technology Data Exchange (ETDEWEB)
Carvalho, M.; Vilar, L.C.Q.; Helayel-Neto, J.A.
1995-10-01
We present a supersymmetric non-linear {sigma}-model built up in the N 1 superspace of Atiyah-ward space-time. A manifold of the Kaehler type comes out that is restricted by a a particular decomposition of the Kaehler potential. The gauging of the {sigma}-model isometries is also accomplished in superspace. (author). 20 refs.
Kitahara, Teppei; Tremper, Paul
2016-01-01
The standard analytic solution of the renormalization group (RG) evolution for the $\\Delta S = 1$ Wilson coefficients involves several singularities. In practical applications one either regularizes these singularities or circumvents the problem by using numerical integrations. In this paper we derive a singularity-free solution of the next-to-leading order (NLO) RG equations, which greatly facilitates the calculation of $\\epsilon_K^{\\prime}$, the measure of direct $CP$ violation in $K\\to\\pi\\pi$ decays. Using our new RG evolution and the latest lattice results for the hadronic matrix elements, we calculate the ratio $\\epsilon_{K}^{\\prime}/\\epsilon_{K}$ (with $\\epsilon_{K}$ quantifying indirect $CP$ violation) in the Standard Model (SM) at NLO to $\\epsilon_{K}^{\\prime}/\\epsilon_{K} = ( 0.96 \\pm 4.96 ) \\times 10^{-4}$, which is 2.9$\\,\\sigma$ below the experimental value. We also present the evolution matrix in the high-energy regime for calculations of new physics contributions and derive easy-to-use approximat...
5D-QSAR for spirocyclic sigma1 receptor ligands by Quasar receptor surface modeling.
Oberdorf, Christoph; Schmidt, Thomas J; Wünsch, Bernhard
2010-07-01
Based on a contiguous and structurally as well as biologically diverse set of 87 sigma(1) ligands, a 5D-QSAR study was conducted in which a quasi-atomistic receptor surface modeling approach (program package Quasar) was applied. The superposition of the ligands was performed with the tool Pharmacophore Elucidation (MOE-package), which takes all conformations of the ligands into account. This procedure led to four pharmacophoric structural elements with aromatic, hydrophobic, cationic and H-bond acceptor properties. Using the aligned structures a 3D-model of the ligand binding site of the sigma(1) receptor was obtained, whose general features are in good agreement with previous assumptions on the receptor structure, but revealed some novel insights since it represents the receptor surface in more detail. Thus, e.g., our model indicates the presence of an H-bond acceptor moiety in the binding site as counterpart to the ligands' cationic ammonium center, rather than a negatively charged carboxylate group. The presented QSAR model is statistically valid and represents the biological data of all tested compounds, including a test set of 21 ligands not used in the modeling process, with very good to excellent accuracy [q(2) (training set, n=66; leave 1/3 out) = 0.84, p(2) (test set, n=21)=0.64]. Moreover, the binding affinities of 13 further spirocyclic sigma(1) ligands were predicted with reasonable accuracy (mean deviation in pK(i) approximately 0.8). Thus, in addition to novel insights into the requirements for binding of spirocyclic piperidines to the sigma(1) receptor, the presented model can be used successfully in the rational design of new sigma(1) ligands. Copyright (c) 2010 Elsevier Masson SAS. All rights reserved.
Developing an integrated model for evaluation and selection of six sigma projects using ANN
Directory of Open Access Journals (Sweden)
Seyed Habib Allah Mirghafoori
2012-03-01
Full Text Available Six Sigma is one of the most popular systems for eliminating waste, reducing cost and improving quality in organizations. The process of evaluation and selection of projects is the first step towards implementing Six Sigma and many researchers believe that these are important for the success of such projects. Respectively, in this paper, a model has been proposed based on artificial neural network (ANN as an effective tool for non-linear information processing . In this model, six criteria of project cost, project duration, number of Black and Green Belts, improving customer satisfaction, impact on business strategy and financial impact have been identified as input factors and productivity and sigma level of improvement projects have been estimated using multi-layer perception (MLP. Finally, sensitivity analysis has been used for evaluation of the influence of inputs on outputs. The findings imply that 'business strategy' and 'financial impact' have the most and the least influence on model's outputs, including productivity and Sigma level, respectively. .
The Density Matrix Renormalization Group Method and Large-Scale Nuclear Shell-Model Calculations
Dimitrova, S S; Pittel, S; Stoitsov, M V
2002-01-01
The particle-hole Density Matrix Renormalization Group (p-h DMRG) method is discussed as a possible new approach to large-scale nuclear shell-model calculations. Following a general description of the method, we apply it to a class of problems involving many identical nucleons constrained to move in a single large j-shell and to interact via a pairing plus quadrupole interaction. A single-particle term that splits the shell into degenerate doublets is included so as to accommodate the physics of a Fermi surface in the problem. We apply the p-h DMRG method to this test problem for two $j$ values, one for which the shell model can be solved exactly and one for which the size of the hamiltonian is much too large for exact treatment. In the former case, the method is able to reproduce the exact results for the ground state energy, the energies of low-lying excited states, and other observables with extreme precision. In the latter case, the results exhibit rapid exponential convergence, suggesting the great promi...
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
Ehlers, G.; White, S. R.; Noack, R. M.
2017-03-01
The performance of the density matrix renormalization group (DMRG) is strongly influenced by the choice of the local basis of the underlying physical lattice. We demonstrate that, for the two-dimensional Hubbard model, the hybrid-real-momentum-space formulation of the DMRG is computationally more efficient than the standard real-space formulation. In particular, we show that the computational cost for fixed bond dimension of the hybrid-space DMRG is approximately independent of the width of the lattice, in contrast to the real-space DMRG, for which it is proportional to the width squared. We apply the hybrid-space algorithm to calculate the ground state of the doped two-dimensional Hubbard model on cylinders of width four and six sites; at n =0.875 filling, the ground state exhibits a striped charge-density distribution with a wavelength of eight sites for both U /t =4.0 and 8.0 . We find that the strength of the charge ordering depends on U /t and on the boundary conditions. Furthermore, we investigate the magnetic ordering as well as the decay of the static spin, charge, and pair-field correlation functions.
Bajc, B.; Blin, A. H.; Hiller, B.; Nemes, M. C.; Rosina, M.
1994-01-01
We calculate the momentum dependence of three particle vertices $\\sigma \\gamma \\gamma$, $\\sigma \\rho \\gamma$ and $\\sigma \\rho \\rho$ in the context of a Nambu Jona Lasinio type model. We show how they influence the processes $\\gamma \\gamma \\rightarrow \\sigma \\rightarrow \\pi \\pi$, $\\rho \\rightarrow \\gamma \\sigma$ and $\\gamma \\gamma \\rightarrow \\rho \\rho$ and how chiral symmetry shadows the presence of the $\\sigma$.
Dynamic Critical Behavior of Multi-Grid Monte Carlo for Two-Dimensional Nonlinear $\\sigma$-Models
Mana, Gustavo; Mendes, Tereza; Pelissetto, Andrea; Sokal, Alan D.
1995-01-01
We introduce a new and very convenient approach to multi-grid Monte Carlo (MGMC) algorithms for general nonlinear $\\sigma$-models: it is based on embedding an $XY$ model into the given $\\sigma$-model, and then updating the induced $XY$ model using a standard $XY$-model MGMC code. We study the dynamic critical behavior of this algorithm for the two-dimensional $O(N)$ $\\sigma$-models with $N = 3,4,8$ and for the $SU(3)$ principal chiral model. We find that the dynamic critical exponent $z$ vari...
Nogawa, Tomoaki; Hasegawa, Takehisa; Nemoto, Koji
2012-09-01
We study the Ising model in a hierarchical small-world network by renormalization group analysis and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP of the ordered phase. The weak stability of the FP yields peculiar criticalities, including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and is continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges upon approaching the transition point.
Is the 2D O(3) Nonlinear $\\sigma$ Model Asymptotically Free?
Patrascioiu, Adrian; Seiler, Erhard
1997-01-01
We report the results of a Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\\sigma$ model. The notable finding is that it agrees very well with both the prediction inspired by Zamolodchikovs' S-matrix ansatz and with the continuum limit of the dodecahedron spin model. The latter finding renders the existence of asymptotic freedom in the O(3) model rather unlikely.
Duclut, Charlie
2016-01-01
We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent $z$. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the Principle of Minimal Sensitivity (PMS) is employed to optimize the critical exponents $\\eta$, $\
Selfduality of d=2 Reduction of Gravity Coupled to a Sigma-Model
Paulot, L
2004-01-01
Dimensional reduction in two dimensions of gravity in higher dimension, or more generally of d=3 gravity coupled to a sigma-model on a symmetric space, is known to possess an infinite number of symmetries. We show that such a bidimensional model can be embedded in a covariant way into a sigma-model on an infinite symmetric space, built on the semidirect product of an affine group by the Witt group. The finite theory is the solution of a covariant selfduality constraint on the infinite model. It has therefore the symmetries of the infinite symmetric space. (We give explicit transformations of the gauge algebra.) The usual physical fields are recovered in a triangular gauge, in which the equations take the form of the usual linear systems which exhibit the integrable structure of the models. Moreover, we derive the constraint equation for the conformal factor, which is associated to the central term of the affine group involved.
Renormalization of seesaw neutrino masses in the standard model with two-Higgs doublets
Indian Academy of Sciences (India)
N Nimai Singh; S Biramani Singh
2000-02-01
Using the theoretical ambiguities inherent in the seesaw mechanism, we derive the new analytic expressions for both quadratic and linear seesaw formulae for neutrino masses at low energies, with either up-type quark masses or charged lepton masses. This is possible through full radiative corrections arising out of the renormalizations of the Yukawa couplings, the coefﬁcients of the neutrino-mass-operator in the standard model with two-Higgs doublets, and also the QCD–QED rescaling factors below the top-quark mass scale, at one-loop level. We also investigate numerically the uniﬁcation of top-- Yukawa couplings at the scale =0.59× 108GeV for a ﬁxed value of tan =58.77, and then evaluate the seesaw neutrino masses which are too large in magnitude to be compatible with the presently available solar and atmospheric neutrino oscillation data. However, if we consider a higher but arbitrary value of =0.59× 1011GeV, the predictions from linear seesaw formulae with charged lepton masses, can accommodate simultaneousely both solar atmospheric neutrino oscillation data.
Tensor Renormalization Group Study of the General Spin-S Blume-Capel Model
Yang, Li-Ping; Xie, Zhi-Yuan
2016-10-01
We focus on the special situation of D = 2J in the general spin-S Blume-Capel model on a square lattice. Under an infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are investigated by the newly developed tensor renormalization group method. We clearly demonstrate the phase transition process: in the case of an integer spin-S, there are S first-order phase transitions with the stepwise magnetizations M = S,S - 1, ldots ,0; in the case of a half-odd integer spin-S, there are S - 1/2 first-order phase transitions with corresponding M = S,S - 1, ldots ,1/2 in addition to one continuous phase transition due to spin-flip Z2 symmetry breaking. At low temperatures, all first-order phase transitions are accompanied by the successive disappearance of the spin-component pairs (±s); furthermore, the transition temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of a magnetic field, a visualization parameter characterizing the intrinsic degeneracy of the different phases provides a different reference for the phase transition process.
Truncating an exact matrix product state for the XY model: Transfer matrix and its renormalization
Rams, Marek M.; Zauner, Valentin; Bal, Matthias; Haegeman, Jutho; Verstraete, Frank
2015-12-01
We discuss how to analytically obtain an essentially infinite matrix product state (MPS) representation of the ground state of the XY model. On one hand this allows us to illustrate how the Ornstein-Zernike form of the correlation function emerges in the exact case using standard MPS language. On the other hand we study the consequences of truncating the bond dimension of the exact MPS, which is also part of many tensor network algorithms, and analyze how the truncated MPS transfer matrix is representing the dominant part of the exact quantum transfer matrix. In the gapped phase we observe that the correlation length obtained from a truncated MPS approaches the exact value following a power law in effective bond dimension. In the gapless phase we find a good match between a state obtained numerically from standard MPS techniques with finite bond dimension and a state obtained by effective finite imaginary time evolution in our framework. This provides a direct hint for a geometric interpretation of finite entanglement scaling at the critical point in this case. Finally, by analyzing the spectra of transfer matrices, we support the interpretation put forward by V. Zauner et al. [New J. Phys. 17, 053002 (2015), 10.1088/1367-2630/17/5/053002] that the MPS transfer matrix emerges from the quantum transfer matrix though the application of Wilson's numerical renormalization group along the imaginary-time direction.
Renormalized. pi. NN coupling constant and the P-italic-wave phase shifts in the cloudy bag model
Energy Technology Data Exchange (ETDEWEB)
Pearce, B.C.; Afnan, I.R.
1986-09-01
Most applications of the cloudy bag model to ..pi..N scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P-italic/sub 11/ channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ..pi pi..N system that incorporate three-body unitarity.
Renormalized πNN coupling constant and the P-wave phase shifts in the cloudy bag model
Pearce, B. C.; Afnan, I. R.
1986-09-01
Most applications of the cloudy bag model to πN scattering involve unitarizing the bare diagrams arising from the Lagrangian by iterating in a Lippmann-Schwinger equation. However, analyses of the renormalization of the coupling constant proceed by iterating the Lagrangian to a given order in the bare coupling constant. These two different approaches means there is an inconsistency between the calculation of phase shifts and the calculation of renormalization. A remedy to this problem is presented that has the added advantage of improving the fit to the phase shifts in the P11 channel. This is achieved by using physical values of the coupling constant in the crossed diagram which reduces the repulsion rather than adds attraction. This approach can be justified by examining equations for the ππN system that incorporate three-body unitarity.
Wu, Yue-Liang
2013-01-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s, its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than and equal to the space-time dimension must vanish. The LORE method is achieved without modi...
Renormalization Group (RG) in Turbulence: Historical and Comparative Perspective
Zhou, Ye; McComb, W. David; Vahala, George
1997-01-01
The term renormalization and renormalization group are explained by reference to various physical systems. The extension of renormalization group to turbulence is then discussed; first as a comprehensive review and second concentrating on the technical details of a few selected approaches. We conclude with a discussion of the relevance and application of renormalization group to turbulence modelling.
Nucleon Properties at Finite Temperature in the Extended Quark-Sigma Model
Abu-Shady, M
2014-01-01
Hadron properties are studied at hot medium using the quark sigma model. The quark sigma model is extended to include eighth-order of mesonic interactions based on some aspects of quantum chromodynamic (QCD) theory. The extended effective potential tends to the original effective potential when the coupling between the higher order mesonic interactions equal to zero. The field equations have been solved in the mean-field approximation by using the extended iteration method. We found that the nucleon mass increases with increasing temperature and the magnetic moments of proton and neutron increase with increasing temperature. A comparison is presented with recent previous works and other models. We conclude that higher-order mesonic interactions play an important role in changing the behavior of nucleon properties at finite temperature. In addition, the deconfinement phase transition is satisfied in the present model.
A geometrical construction of rational boundary states in linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Kennaway, Kristian D. E-mail: kennaway@usc.edu
2002-12-30
Starting from the geometrical construction of special Lagrangian submanifolds of a toric variety, we identify a certain subclass of A-type D-branes in the linear sigma model for a Calabi-Yau manifold and its mirror with the A- and B-type Recknagel-Schomerus boundary states of the Gepner model, by reproducing topological properties such as their labeling, intersection, and the relationships that exist in the homology lattice of the D-branes. In the non-linear sigma model phase these special Lagrangians reproduce an old construction of 3-cycles relevant for computing periods of the Calabi-Yau, and provide insight into other results in the literature on special Lagrangian submanifolds on compact Calabi-Yau manifolds. The geometrical construction of rational boundary states suggests several ways in which new Gepner model boundary states may be constructed.
Directory of Open Access Journals (Sweden)
V. Bacsó
2015-12-01
Full Text Available In this paper we study the c-function of the sine-Gordon model taking explicitly into account the periodicity of the interaction potential. The integration of the c-function along trajectories of the non-perturbative renormalization group flow gives access to the central charges of the model in the fixed points. The results at vanishing frequency β2, where the periodicity does not play a role, are retrieved and the independence on the cutoff regulator for small frequencies is discussed. Our findings show that the central charge obtained integrating the trajectories starting from the repulsive low-frequencies fixed points (β2<8π to the infra-red limit is in good quantitative agreement with the expected Δc=1 result. The behavior of the c-function in the other parts of the flow diagram is also discussed. Finally, we point out that including also higher harmonics in the renormalization group treatment at the level of local potential approximation is not sufficient to give reasonable results, even if the periodicity is taken into account. Rather, incorporating the wave-function renormalization (i.e. going beyond local potential approximation is crucial to get sensible results even when a single frequency is used.
Palma, G; Zambrano, D
2008-12-01
In this paper we propose a method to study critical systems numerically, which combines collective-mode algorithms and renormalization group on the lattice. This method is an improved version of the Monte Carlo renormalization group in the sense that it has all the advantages of cluster algorithms. As an application we considered the 2D Ising model and studied whether scale invariance or universality are possible underlying mechanisms responsible for the approximate "universal fluctuations" close to a so-called bulk temperature T(L) . "Universal fluctuations" were first proposed in the work of Bramwell, Holdsworth, and Pinton [Nature (London) 396, 552 (1998)] and stated that the probability density function of a global quantity for very dissimilar systems, such as a confined turbulent flow and a two-dimensional (2D) magnetic system, properly normalized to the first two moments, becomes similar to the "universal distribution," originally obtained for magnetization in the 2D XY model in the low-temperature region. The results for the critical exponents and the renormalization-group flow of the probability density function are very accurate and show no evidence to support that the approximate common shape of the PDF should be related to both scale invariance or universal behavior.
Scaling in erosion of landscapes: renormalization group analysis of a model with turbulent mixing
Antonov, N. V.; Kakin, P. I.
2017-02-01
The model of landscape erosion, introduced in (1998 Phys. Rev. Lett. 80 4349, 1998 J. Stat. Phys. 93 477) and modified in (2016 Theor. Math. Phys. in press (arXiv:1602.00432)), is advected by anisotropic velocity field. The field is Gaussian with vanishing correlation time and the pair correlation function of the form \\propto δ ≤ft(t-{{t}\\prime}\\right)/k\\botd-1+ξ , where {{k}\\bot}=|{{\\mathbf{k}}\\bot}| and {{\\mathbf{k}}\\bot} is the component of the wave vector, perpendicular to a certain preferred direction—the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda (1990 Commun. Math. Phys. 131 381). Analogous to the case without advection, the model is multiplicatively renormalizable and has infinitely many coupling constants. The one-loop counterterm is derived in a closed form in terms of the certain function V(h), entering the original stochastic equation, and its derivatives with respect to the height field h≤ft(t,\\mathbf{x}\\right) . The full infinite set of the one-loop renormalization constants, β-functions and anomalous dimensions is obtained from the Taylor expansion of the counter-term. Instead of a two-dimensional surface of fixed points there are two such surfaces; they are likely to contain infrared attractive region(s). If that is the case, the model exhibits scaling behaviour in the infrared range. The corresponding critical exponents are non-universal because they depend on the coordinates of the fixed points on the surface; they also satisfy certain universal exact relation.
Suzuki-Trotter decomposition and renormalization of a transverse-field Ising model in two dimensions
Dudziński, M.; Sznajd, J.
1997-06-01
The combined Suzuki-Trotter decomposition and Niemeijer-van Leuween real-space renormalization-group techniques are used to study the critical properties of a two-dimensional Ising system with a transverse field. The inverse critical temperature as a function of the external field and the temperature dependence of the transverse component of the magnetization are found. It is also shown that any real-space renormalization-group procedure based on the simple generalization of the Niemeijer-van Leeuwen majority rule for one of the components of the total-cell spin does not preserve the symmetry of the quantum spin space.
Resurgence and dynamics of O(N) and Grassmannian sigma models
Dunne, Gerald V.; Ünsal, Mithat
2015-09-01
We study the non-perturbative dynamics of the two dimensional O( N ) and Grassmannian sigma models by using compactification with twisted boundary conditions on {R}× {S}^1 , semi-classical techniques and resurgence. While the O( N) model has no instantons for N > 3, it has (non-instanton) saddles on {{R}}^2 , which we call 2d-saddles. On {R}× {S}^1 , the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o( N ) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O( N ) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO( N ) gauge theory on {{R}}^3× {S}^1 . The Grassmannian sigma models Gr( N, M ) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr( N, M ), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes, providing a microscopic argument for Haldane's conjecture.
AdS5×S(5) mirror model as a string sigma model.
Arutyunov, Gleb; van Tongeren, Stijn J
2014-12-31
Doing a double Wick rotation in the world sheet theory of the light cone AdS5×S(5) superstring results in an inequivalent, so-called mirror theory that plays a central role in the field of integrability in the AdS-CFT correspondence. We show that this mirror theory can be interpreted as the light cone theory of a free string on a different background. This background is related to dS5×H(5) by a double T-duality, and has hidden supersymmetry. The geometry can also be extracted from an integrable deformation of the AdS5×S(5) sigma model, and we prove the observed mirror duality of these deformed models at the bosonic level as a byproduct. While we focus on AdS5×S(5), our results apply more generally.
All-loop correlators of integrable $\\lambda$-deformed $\\sigma$-models
Georgiou, George; Siampos, Konstantinos
2016-01-01
We compute the 2- and 3-point functions of currents and primary fields of $\\lambda$-deformed integrable $\\sigma$-models characterized also by an integer $k$. Our results apply for any semisimple group $G$, for all values of the deformation parameter $\\lambda$ and up to order $1/k$. We deduce the OPEs and equal-time commutators of all currents and primaries. We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable $\\lambda$-deformed $\\sigma$-models. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.
Madjumdar-Papapetrou Type Solutions in Sigma-model and Intersecting p-branes
Ivashchuk, V D
1999-01-01
The block-orthogonal generalization of the Madjumdar-Papapetrou type solutions for the sigma-model studied earlier in \\cite{IM4}-\\cite{IMC} are obtained and corresponding solutions with p-branes are considered. The existence of solutions and the number of independent harmonic functions is defined by the matrix of scalar products of vectors $U^s$, governing the sigma-model target space metric. (For orthogonal $U^s$, when target space is symmetric homogeneous space, the solutions coincide with those from finite dimensional Lie algebras and hyperbolic (Kac-Moody) algebras are singled out and investigated. The affine Cartan matrices do not arise in the scheme under consideration. Some examples of solutions and intersection rules for D=11 supergravity, related D=12 theory and extending them $B_D$-models are considered. For special multicenter solutions the indicators of horizon and curvature singularity are introduced.
The quark-meson coupling model for $\\Lambda$, $\\Sigma$ and $\\Xi$ hypernuclei
Tsushima, K; Haidenbauer, J; Thomas, A W
1998-01-01
The quark-meson coupling (QMC) model, which has been successfully used to describe the properties of both infinite nuclear matter and finite nuclei, is applied to a systematic study of $\\Lambda, \\Sigma$ and $\\Xi$ hypernuclei. Assumptions made in the present study are, (i) the (self-consistent) exchanged scalar, and vector, mesons couple only to the u and d quarks, and (ii) an SU(6) valence quark model for the bound nucleons and hyperon. The model automatically leads to a very weak spin-orbit interaction for the $\\Lambda$ in a hypernucleus. Effects of the Pauli blocking at the quark level, and the $\\Sigma N - \\Lambda N$ channel coupling (strong conversion), are also taken into account in a phenomenological way.
Nonequilibrium dynamics of the O(N) linear sigma model
Michalski, S
2003-01-01
We investigate the out-of-equilibrium evolution of a classical background field and its quantum fluctuations in the scalar O(N) model with spontaneous symmetry breaking. We consider the 2-loop 2PI effective action in the Hartree approximation, i.e., including bubble resummation but without non-local contributions to the Dyson-Schwinger equation. We concentrate on the (nonequilibrium) phase structure of the model and observe a first-order transition between a spontaneously broken and a symmetric phase at low and high energy densities, respectively. So typical structures expected in thermal equilibrium are encountered in nonequilibrium dynamics even at early times before thermalization.
Tawfik, Abdel Nasser; Hussein, M T
2016-01-01
In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$\\sigma$ model (PLSM) is analysed for chiral phase-transition, $\\sigma_l$ and $\\sigma_s$ and for deconfinement order-parameters, $\\phi$ and $\\phi^*$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates ($\\Delta_{l,s}$). All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modelling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric [$\\sigma_{el}(T)$] and heat [$\\kappa(T)$] conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, $\\xi/s$...
Droplets in the cold and dense linear sigma model with quarks
Palhares, Leticia F
2010-01-01
The linear sigma model with quarks at very low temperatures provides an effective description for the thermodynamics of the strong interaction in cold and dense matter, being especially useful at densities found in compact stars and protoneutron star matter. Using the MSbar one-loop effective potential, we compute quantities that are relevant in the process of nucleation of droplets of quark matter in this scenario. In particular, we show that the model predicts a surface tension of \\Sigma ~ 5-15 MeV/fm^2, rendering nucleation of quark matter possible during the early post-bounce stage of core collapse supernovae. Including temperature effects and vacuum logarithmic corrections, we find a clear competition between these features in characterizing the dynamics of the chiral phase conversion, so that if the temperature is low enough the consistent inclusion of vacuum corrections could help preventing the nucleation of quark matter during the collapse process. We also discuss the first interaction corrections th...
T-duality transformation of gauged linear sigma model with F-term
Directory of Open Access Journals (Sweden)
Tetsuji Kimura
2014-10-01
Full Text Available We develop the duality transformation rules in two-dimensional theories in the superfield formalism. Even if the chiral superfield which we dualize involves an F-term, we can dualize it by virtue of the property of chiral superfields. We apply the duality transformation rule of the neutral chiral superfield to the N=(4,4 gauged linear sigma model for five-branes. We also investigate the duality transformation rule of the charged chiral superfield in the N=(4,4 gauged linear sigma model for the A1-type ALE space. In both cases we obtain the dual Lagrangians in the superfield formalism. In the low energy limit we find that their duality transformations are interpreted as T-duality transformations consistent with the Buscher rule.
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Kohno, M; Kawai, M; Ogata, K; Watanabe, Y
2006-01-01
$(\\pi^-,K^+)$ hyperon production inclusive spectra with $p_\\pi =1.2$ GeV/c measured at KEK on $^{12}$C and $^{28}$Si are analyzed by the semiclassical distorted wave model. Single-particle wave functions of the target nucleus are treated using Wigner transformation. This method is able to account for the energy and angular dependences of the elementary process in nuclear medium without introducing the factorization approximation frequently employed. Calculations of the $(\\pi^+,K^+)$ $\\Lambda$ formation process, for which there is no free parameter since the $\\Lambda$ s.p. potential is known, demonstrate that the present model is useful to describe inclusive spectra. It is shown that in order to account for the experimental data of the $\\Sigma^-$ formation spectra a repulsive $\\Sigma$-nucleus potential is necessary whose magnitude is not so strong as around 100 MeV previously suggested.
Directory of Open Access Journals (Sweden)
N. V. R. Naidu
2011-09-01
Full Text Available This paper deals with a critical evaluation of the Preventive Maintenance system in steel industry. This study helps in implementing Six Sigma solutions to reduce the down time of two critical machines i.e., Electric Arc Furnace (EAF and Billet Casting Machine (BCM. It is clear from the analysis of EAF and BCM respectively that, variations in output are quite possible because the machines output not only depend on maintenance time but also on several other variables. Further, the objective is to design a preventive maintenance programme on the same equipment situated in the plant using Six Sigma. The breakdown of these equipments could very well affect the production rate. For this, the mathematical models have been developed and these models are used to obtain the optimum preventive maintenance frequency for minimizing the down time and maximizing the profits.
T-duality Transformation of Gauged Linear Sigma Model with F-term
Kimura, Tetsuji
2014-01-01
We develop the duality transformation rules in two-dimensional theories in the superfield formalism. Even if the chiral superfield which we dualize is involved in F-term, we can convert the F-term to D-terms by virtue of the property of chiral superfields. We apply the duality transformation rule of the neutral chiral superfield to the ${\\cal N}=(4,4)$ gauged linear sigma model for five-branes. We also investigate the duality transformation rule of the charged chiral superfield in the ${\\cal N} = (4,4)$ gauged linear sigma model for the $A_1$-type ALE space. In both cases we obtain the dual Lagrangians in the superfield formalism. In the low energy limit we find that their duality transformations are interpreted as the T-duality transformations consistent with the Buscher rule.
On Symmetries of Target Space for $\\sigma$-model of p-brane Origin
Ivashchuk, V D
1998-01-01
The target space M for the sigma-model appearing in theories with p-branes is considered. It is proved that M is a homogeneous space G/H. It is symmetric if and only if the U-vectors governing the sigma-model metric are either coinciding or mutually orthogonal. For nonzero noncoinciding U-vectors the Killing equations are solved. Using a block-orthogonal decomposition of the set of the U-vectors it is shown that under rather general assumptions the algebra of Killing vectors is a direct sum of several copies of sl(2,R) algebras (corresponding to 1-vector blocks), several solvable Lie algebras (corresponding to multivector blocks) and the Killing algebra of a flat space. The target space manifold is decomposed in a product of R^m, several 2-dimensional spaces of constant curvature (e.g. Lobachevsky space, part of de Sitter space) and several solvable Lie group manifolds.
Free Differential Algebras and Pure Spinor Action in IIB Superstring Sigma Models
Oda, Ichiro
2011-01-01
In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts $\\lambda $ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superstrings in curved supergravity backgrounds (on shell), in full agreement with the action first obtained by Berkovits and Howe.
Free differential algebras and pure spinor action in IIB superstring sigma models
Oda, Ichiro; Tonin, Mario
2011-06-01
In this paper we extend to the case of IIB superstring sigma models the method proposed in hep-th/10023500 to derive the pure spinor approach for type IIA sigma models. In particular, starting from the (Free) Differential Algebra and superspace parametrization of type IIB supergravity, extended to include the BRST differential and all the ghosts, we derive the BRST transformations of fields and ghosts as well as the standard pure spinor constraints for the ghosts λ related to supersymmetry. Moreover, using the method first proposed by us, we derive the pure spinor action for type IIB superstrings in curved supergravity backgrounds (on shell), in full agreement with the action first obtained by Berkovits and Howe.
Oksala, M E; Townsend, R H D; Owocki, S P; Kochukhov, O; Neiner, C; Alecian, E; Grunhut, J
2011-01-01
We have obtained 18 new high-resolution spectropolarimetric observations of the B2Vp star sigma Ori E with both the Narval and ESPaDOnS spectropolarimeters. The aim of these observations is to test, with modern data, the assumptions of the Rigidly Rotating Magnetosphere (RRM) model of Townsend & Owocki (2005), applied to the specific case of sigma Ori E by Townsend et al. (2005). This model includes a substantially offset dipole magnetic field configuration, and approximately reproduces previous observational variations in longitudinal field strength, photometric brightness, and Halpha emission. We analyze new spectroscopy, including H I, He I, C II, Si III and Fe III lines, confirming the diversity of variability in photospheric lines, as well as the double S-wave variation of circumstellar hydrogen. Using the multiline analysis method of Least-Squares Deconvolution (LSD), new, more precise longitudinal magnetic field measurements reveal a substantial variance between the shapes of the observed and RRM m...
Excited state TBA and renormalized TCSA in the scaling Potts model
Lencses, M
2014-01-01
We consider the field theory describing the scaling limit of the Potts quantum spin chain using a combination of two approaches. The first is the renormalized truncated conformal space approach (TCSA), while the second one is a new thermodynamic Bethe Ansatz (TBA) system for the excited state spectrum in finite volume. For the TCSA we investigate and clarify several aspects of the renormalization procedure and counter term construction. The TBA system is first verified by comparing its ultraviolet limit to conformal field theory and the infrared limit to exact S-matrix predictions. We then show that the TBA and the renormalized TCSA match each other to a very high precision for a large range of the volume parameter, providing both a further verification of the TBA system and a demonstration of the efficiency of the TCSA renormalization procedure. We also discuss the lessons learned from our results concerning recent developments regarding the low-energy scattering of quasi-particles in the quantum Potts spin ...
Institute of Scientific and Technical Information of China (English)
LIU Zheng-Feng; WANG Xiao-Hong
2008-01-01
Adopting Yoshizawa's two-scale expansion technique,the fluctuating field is expanded around the isotropic field.The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion,A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically.Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa,the calculation is much more simple.The analytical model presented here is close to the Speziale model,which is widely applied in the numerical simulations for the complex turbulent flows.
Renormalization Scheme Dependence and Renormalization Group Summation
McKeon, D G C
2016-01-01
We consider logarithmic contributions to the free energy, instanton effective action and Laplace sum rules in QCD that are a consequence of radiative corrections. Upon summing these contributions by using the renormalization group, all dependence on the renormalization scale parameter mu cancels. The renormalization scheme dependence in these processes is examined, and a renormalization scheme is found in which the effect of higher order radiative corrections is absorbed by the behaviour of the running coupling.
Chaotic renormalization-group trajectories
DEFF Research Database (Denmark)
Damgaard, Poul H.; Thorleifsson, G.
1991-01-01
, or in regions where the renormalization-group flow becomes chaotic. We present some explicit examples of these phenomena for the case of a Lie group valued spin-model analyzed by means of a variational real-space renormalization group. By directly computing the free energy of these models around the parameter......Under certain conditions, the renormalization-group flow of models in statistical mechanics can change dramatically under just very small changes of given external parameters. This can typically occur close to bifurcations of fixed points, close to the complete disappearance of fixed points...... regions in which such nontrivial modifications of the renormalization-group flow occur, we can extract the physical consequences of these phenomena....
All $(4,1)$: Sigma Models with $(4,q)$ Off-Shell Supersymmetry
Hull, Chris
2016-01-01
Off-shell $(4,q)$ supermultiplets in 2-dimensions are constructed for $q=1,2,4$. These are used to construct sigma models whose target spaces are hyperk\\"ahler with torsion. The off-shell supersymmetry implies the three complex structures are simultaneously integrable and allows us to construct actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.
Boundary coupling of Lie algebroid Poisson sigma models and representations up to homotopy
Velez, Alexander Quintero
2011-01-01
A general form for the boundary coupling of a Lie algebroid Poisson sigma model is proposed. The approach involves using the Batalin-Vilkovisky formalism in the AKSZ geometrical version, to write a BRST-invariant coupling for a representation up to homotopy of the target Lie algebroid or its subalgebroids. These considerations lead to a conjectural description of topological D-branes on generalized complex manifolds, which includes A-branes and B-branes as special cases.
Heterotic sigma models on $T^8$ and the Borcherds automorphic form $\\Phi_{12}$
Harrison, Sarah M; Paquette, Natalie M; Volpato, Roberto; Zimet, Max
2016-01-01
We consider the spectrum of BPS states of the heterotic sigma model with $(0,8)$ supersymmetry and $T^8$ target, as well as its second-quantized counterpart. We show that the counting function for such states is intimately related to Borcherds' automorphic form $\\Phi_{12}$, a modular form which exhibits automorphy for $O(2,26;{\\mathbb Z})$. We comment on possible implications for Umbral moonshine and theories of AdS$_3$ gravity.
All (4,0): Sigma models with (4,0) off-shell supersymmetry
Hull, Chris; Lindström, Ulf
2017-08-01
Off-shell (4, 0) supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions using extended superspace and projective superspace, giving an explicit construction of the target space geometries.
Flat Currents and Solutions of Sigma Model on Supercoset Targets with Z2m Grading
Institute of Scientific and Technical Information of China (English)
KE san-Min; SHI Kang-Jie; WANG Chun; WU Sheng
2007-01-01
We find one parameter flat currents of the sigma model on supercoset targets with Z2m grading given by Young satisfaction equations of motion and the Virasoro constraint.This meads that one can generate a series of classical solutions from the original one.For these new solutions one can also construct flat currents and conserved charges,which form the same set with the original one.
Kong, Kook-Jin; Yu, Byung-Geel
2016-01-01
We investigate the role driven by the $\\sigma$ exchange in the photoproduction of $\\phi$ meson off a proton by using the Reggeized model. In this reaction, in addition to the Pomeron exchange which constitutes the background contribution extending to high energies, the $\\sigma$ Regge-pole exchange is found to give an interesting contribution to the reaction process near threshold. In particular, the $\\sigma$ exchange can reproduce reasonably well the bump structure at the forward angle in the differential cross section as well as the peaking behavior in the total cross section observed in the CLAS collaboration. We also show that our calculation reproduces well the recent data for the differential cross section from the LEPS and CLAS at low energies. Moreover, the scaled cross section $s^7d\\sigma /dt$ at the production angle $\\theta=90^{\\circ}$ obtained from the CLAS data is found to be consistent with the calculation using the canonical phase of the $\\sigma$ Regge-pole.
Pion-Nucleon Scattering in a Large-N Sigma Model
Mattis, M P; MATTIS, Michael P.; SILBAR, Richard R.
1995-01-01
We review the large-N_c approach to meson-baryon scattering, including recent interesting developments. We then study pion-nucleon scattering in a particular variant of the linear sigma-model, in which the couplings of the sigma and pi mesons to the nucleon are echoed by couplings to the entire tower of I=J baryons (including the Delta) as dictated by large-N_c group theory. We sum the complete set of multi-loop meson-exchange \\pi N --> \\pi N and \\pi N --> \\sigma N Feynman diagrams, to leading order in 1/N_c. The key idea, reviewed in detail, is that large-N_c allows the approximation of LOOP graphs by TREE graphs, so long as the loops contain at least one baryon leg; trees, in turn, can be summed by solving classical equations of motion. We exhibit the resulting partial-wave S-matrix and the rich nucleon and Delta resonance spectrum of this simple model, comparing not only to experiment but also to pion-nucleon scattering in the Skyrme model. The moral is that much of the detailed structure of the meson-bary...
N=(4,4) Gauged Linear Sigma Models for Defect Five-branes
Kimura, Tetsuji
2015-01-01
We study two-dimensional ${\\cal N}=(4,4)$ gauged linear sigma model (GLSM). Its low energy effective theory is a nonlinear sigma model whose target space gives rise to a configuration of five-branes in string theory. In this article we focus on sigma models for NS5-branes, KK5-branes and an exotic $5^2_2$-brane. In particular, we carefully analyze the GLSM for an exotic $5^2_2$-brane whose background configuration is multi-valued. The exotic $5^2_2$-brane is a concrete example of nongeometric configuration in string theory. We find that the exotic feature originates from the string winding coordinate in a very clear way. In order to complete this analysis, we propose a duality transformation formula which converts an ${\\cal N}=(2,2)$ chiral superfield in F-term to a twisted chiral superfield coupled to an unconstrained complex superfield. This article is a short review based on arXiv:1304.4061 in collaboration with Shin Sasaki.
Nonlinear sigma models with AdS supersymmetry in three dimensions
Butter, Daniel; Tartaglino-Mazzucchelli, Gabriele
2012-01-01
In three-dimensional anti-de Sitter (AdS) space, there exist several realizations of N-extended supersymmetry, which are traditionally labelled by two non-negative integers p>=q such that p+q=N. Different choices of p and q, with N fixed, prove to lead to different restrictions on the target space geometry of supersymmetric nonlinear sigma-models. We classify all possible types of hyperkahler target spaces for the cases N=3 and N=4 by making use of two different realizations for the most general (p,q) supersymmetric sigma-models: (i) off-shell formulations in terms of N=3 and N=4 projective supermultiplets; and (ii) on-shell formulations in terms of covariantly chiral scalar superfields in (2,0) AdS superspace. Depending on the type of N=3,4 AdS supersymmetry, nonlinear sigma-models can support one of the following target space geometries: (i) hyperkahler cones; (ii) non-compact hyperkahler manifolds with a U(1) isometry group which acts non-trivially on the two-sphere of complex structures; (iii) arbitrary h...
On symmetries of N=(4,4) sigma models on T^4
Volpato, Roberto
2014-01-01
Motivated by an analogous result for K3 models, we classify all groups of symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4) superconformal algebra. The resulting symmetry groups are isomorphic to certain subgroups of the Weyl group of E8, that plays a role similar to the Conway group for the case of K3 models. Our analysis heavily relies on the triality automorphism of the T-duality group SO(4,4,Z). As a byproduct of our results, we discover new explicit descriptions of K3 models as asymmetric orbifolds of torus CFTs.
Relating harmonic and projective descriptions of N=2 nonlinear sigma models
Butter, Daniel
2012-01-01
Recent papers have established the relationship between projective superspace and a complexified version of harmonic superspace. We extend this construction to the case of general nonlinear sigma models in both frameworks. Using an analogy with Hamiltonian mechanics, we demonstrate how the Hamiltonian structure of the harmonic model and the symplectic structure of the projective model naturally arise from a single unifying action on a complexified version of harmonic superspace. This links the harmonic and projective descriptions of hyperkahler target spaces. For two examples, we show how to derive the projective superspace solutions for the Taub-NUT and Eguchi-Hanson models from the harmonic superspace solutions.
De Lyra, J L; Foong, S K; Gallivan, T E; Harrington, R; Kapulkin, A; Myers, E; Polchinski, Joseph; Lyra, Jorge de; Witt, Bryce De; Foong, See Kit; Gallivan, Timothy; Harrington, Rob; Kapulkin, Arie; Myers, Eric; Polchinski, Joseph
1992-01-01
The nonlinear sigma model for which the field takes its values in the coset space $O(1,2)/O(2)\\times Z_2$ is similar to quantum gravity in being perturbatively nonrenormalizable and having a noncompact curved configuration space. It is therefore a good model for testing nonperturbative methods that may be useful in quantum gravity, especially methods based on lattice field theory. In this paper we develop the theoretical framework necessary for recognizing and studying a consistent nonperturbative quantum field theory of the $O(1,2)/O(2)\\times Z_2$ model. We describe the action, the geometry of the configuration space, the conserved Noether currents, and the current algebra, and we construct a version of the Ward-Slavnov identity that makes it easy to switch from a given field to a nonlinearly related one. Renormalization of the model is defined via the effective action and via current algebra. The two definitions are shown to be equivalent. In a companion paper we develop a lattice formulation of the theory ...
Renormalization automated by Hopf algebra
Broadhurst, D J
1999-01-01
It was recently shown that the renormalization of quantum field theory is organized by the Hopf algebra of decorated rooted trees, whose coproduct identifies the divergences requiring subtraction and whose antipode achieves this. We automate this process in a few lines of recursive symbolic code, which deliver a finite renormalized expression for any Feynman diagram. We thus verify a representation of the operator product expansion, which generalizes Chen's lemma for iterated integrals. The subset of diagrams whose forest structure entails a unique primitive subdivergence provides a representation of the Hopf algebra ${\\cal H}_R$ of undecorated rooted trees. Our undecorated Hopf algebra program is designed to process the 24,213,878 BPHZ contributions to the renormalization of 7,813 diagrams, with up to 12 loops. We consider 10 models, each in 9 renormalization schemes. The two simplest models reveal a notable feature of the subalgebra of Connes and Moscovici, corresponding to the commutative part of the Hopf ...
Modeling of structural and thermodynamics properties of sigma-phase for the Fe-Cr system
Directory of Open Access Journals (Sweden)
Udovskya A.
2012-01-01
Full Text Available The three- sub-lattice model (3SLM for description of atom’s distribution of two components with different coordination numbers (12, 14 and 15, into s-phase structure depended on composition and temperature is depictured in this paper. Energetic parameters of 3SLM were calculated by fitting procedure fixed to results obtained by ab-initio calculations conducted for paramagnetic states of differently ordered complexes stayed at the sigma-phase’s crystal structure for Fe-Cr system at 0 K. Respective algorithm and computer program have allowed to calculate an atom distribution of components upon the sub-lattices of s-phase at 300 - 1100 K. There is satisfactory agreement between calculated results and the experimental data obtained by neutron and structural research methods. Obtained results demonstrate satisfactory agreement between calculated and experimental data of BCC solutions and sigma - phase of the Fe-Cr system stayed at an equilibrium state.
Development of a Mathematical Model for Multivariate Process by Balanced Six Sigma
Directory of Open Access Journals (Sweden)
Díaz-Castellanos Elizabeth Eugenia
2015-07-01
Full Text Available The Six Sigma methodology is widely used in business to improve quality, increase productivity and lower costs, impacting on business improvement. However, today the challenge is to use those tools for improvements that will have a direct impact on the differentiation of value, which requires the alignment of Six Sigma with the competitive strategies of the organization.Hence the importance of a strategic management system to measure, analyze, improve and control corporate performance, while setting out responsibilities of leadership and commitment. The specific purpose of this research is to provide a mathematical model through the alignment of strategic objectives (Balanced Scorecard and tools for productivity improvement (Six Sigma for processes with multiple answers, which is sufficiently robust so that it can serve as basis for application in manufacturing and thus effectively link strategy performance and customer satisfaction. Specifically we worked with a case study: Córdoba, Ver. The model proposes that is the strategy, performance and customer satisfaction are aligned, the organization will benefit from the intense relationship between process performance and strategic initiatives. These changes can be measured by productivity and process metrics such as cycle time, production rates, production efficiency and percentage of reprocessing, among others.
Polyakov SU(3) extended linear $\\sigma$-model: Sixteen mesonic states in chiral phase-structure
Tawfik, Abdel Nasser
2014-01-01
The derivative of the grand potential in mean field approximation, non-strange and strange condensates and deconfinement phase-transition in thermal and dense hadronic medium are verified in extended SU(3) linear sigma-model (eLSM). In determining the chiral phase-transition, the chiral condensates sigma_x and sigma_y are analysed. The chiral mesonic phase-structures in temperature- and density-dependence are taken as free parameters to be fitted. These parameters are classified corresponding to scalar meson nonets; (pseudo)-scalar and (axial)-vector. For deconfinement phase-transition, effective Polyakov loop-potentials phi and phi^* are utilized. We investigated the in-medium effects on the masses of sixteen mesonic states states. The results are presented for two different forms for the effective Polyakov loop-potential and compared with other models with and without anomalous terms. The Polyakov loop potential in LSM has considerable effects on the chiral phase-transition in meson masses so that the resto...
The cancellation of world-sheet anomalies in the D=10 Green-Schwarz heterotic string sigma model
Energy Technology Data Exchange (ETDEWEB)
Lechner, K. [Padua Univ. (Italy). Dipt. di Fisica; Tonin, M. [Padua Univ. (Italy). Dipt. di Fisica
1996-09-16
We determine the two-dimensional Weyl, Lorentz and {kappa}-anomalies in the D=10 Green-Schwarz heterotic string sigma model, in an SO(1,9) Lorentz-covariant background gauge, and prove their cancellation. (orig.).
Gover, A Rod
2016-01-01
For any conformally compact manifold with hypersurface boundary we define a canonical renormalized volume functional and compute an explicit, holographic formula for the corresponding anomaly. For the special case of asymptotically Einstein manifolds, our method recovers the known results. The anomaly does not depend on any particular choice of regulator, but the coefficients of divergences do. We give explicit formulae for these divergences valid for any choice of regulating hypersurface; these should be relevant to recent studies of quantum corrections to entanglement entropies. The anomaly is expressed as a conformally invariant integral of a local Q-curvature that generalizes the Branson Q-curvature by including data of the embedding. In each dimension this canonically defines a higher dimensional generalization of the Willmore energy/rigid string action. We show that the variation of these energy functionals is exactly the obstruction to solving a singular Yamabe type problem with boundary data along the...
Vidal, G
2007-11-30
We propose a real-space renormalization group (RG) transformation for quantum systems on a D-dimensional lattice. The transformation partially disentangles a block of sites before coarse-graining it into an effective site. Numerical simulations with the ground state of a 1D lattice at criticality show that the resulting coarse-grained sites require a Hilbert space dimension that does not grow with successive RG transformations. As a result we can address, in a quasi-exact way, tens of thousands of quantum spins with a computational effort that scales logarithmically in the system's size. The calculations unveil that ground state entanglement in extended quantum systems is organized in layers corresponding to different length scales. At a quantum critical point, each relevant length scale makes an equivalent contribution to the entanglement of a block.
Calabi-Yau Black Holes and (0,4) Sigma Models
Minasian, Ruben; Moore, Gregory; Tsimpis, Dimitrios
When an M-theory fivebrane wraps a holomorphic surface ? in a Calabi-Yau 3-fold X the low energy dynamics is that of a black string in 5 dimensional ? =1 supergravity. The infrared dynamics on the string worldsheet is an ? = (0,4) 2D conformal field theory. Assuming the 2D CFT can be described as a nonlinear sigma model, we describe the target space geometry of this model in terms of the data of X and ?. Variations of weight two Hodge structures enter the construction of the model in an interesting way.
De Lyra, J L; Foong, S K; Gallivan, T E; Harrington, R; Kapulkin, A; Myers, E; Polchinski, Joseph; Lyra, Jorge de; Witt, Bryce De; Foong, See Kit; Gallivan, Timothy; Harrington, Rob; Kapulkin, Arie; Myers, Eric; Polchinski, Joeseph
1992-01-01
A lattice formulation of the $O(1,2)/O(2)\\times Z_2$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the ``geodesic'' action) that is appropriate for fields having noncompact curved configuration spaces. A consistent continuum limit of the model exists only if the renormalized scale constant $\\beta_R$ vanishes for some value of the bare scale constant~$\\beta$. The geodesic action has a special form that allows direct access to the small-$\\beta$ limit. In this limit half of the degrees of freedom can be integrated out exactly. The remaining degrees of freedom are those of a compact model having a $\\beta$-independent action which is noteworthy in being unbounded from below yet yielding integrable averages. Both the exact action and the $\\beta$-independent action are used to obtain $\\beta_R$ from Monte Carlo computations of field-field averages (2-point functions) and current-current averages. Many consistency cros...
Renormalization and small-world model of fractal quantum repeater networks
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. PMID:23386977
Renormalization and small-world model of fractal quantum repeater networks.
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
Integrability of a family of quantum field theories related to sigma models
Ridout, D
2011-01-01
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2|1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS_2 x S^2, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space.
Integrability of a family of quantum field theories related to sigma models
Energy Technology Data Exchange (ETDEWEB)
Ridout, David, E-mail: david.ridout@anu.edu.au [Department of Theoretical Physics, Australian National University, Canberra, ACT 0200 (Australia); Theory Group, DESY, Notkestrasse 85, D-22603, Hamburg (Germany); Teschner, Joerg [Theory Group, DESY, Notkestrasse 85, D-22603, Hamburg (Germany)
2011-12-11
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2|1) Toda theory, and the N=2 supersymmetric sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS{sub 2}xS{sup 2}, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space.
Integrability of a family of quantum field theories related to sigma models
Energy Technology Data Exchange (ETDEWEB)
Ridout, David [Australian National Univ., Canberra, ACT (Australia). Dept. of Theoretical Physics; DESY, Hamburg (Germany). Theory Group; Teschner, Joerg [DESY, Hamburg (Germany). Theory Group
2011-03-15
A method is introduced for constructing lattice discretizations of large classes of integrable quantum field theories. The method proceeds in two steps: The quantum algebraic structure underlying the integrability of the model is determined from the algebra of the interaction terms in the light-cone representation. The representation theory of the relevant quantum algebra is then used to construct the basic ingredients of the quantum inverse scattering method, the lattice Lax matrices and R-matrices. This method is illustrated with four examples: The Sinh-Gordon model, the affine sl(3) Toda model, a model called the fermionic sl(2 vertical stroke 1) Toda theory, and the N=2 supersymmetric Sine-Gordon model. These models are all related to sigma models in various ways. The N=2 supersymmetric Sine-Gordon model, in particular, describes the Pohlmeyer reduction of string theory on AdS{sub 2} x S{sup 2}, and is dual to a supersymmetric non-linear sigma model with a sausage-shaped target space. (orig.)
Real-space renormalization group study of the Hubbard model on a non-bipartite lattice
Directory of Open Access Journals (Sweden)
R. D. Levine
2002-01-01
Full Text Available Abstract: We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t Ã¢Â‰Âˆ 12.5.
O'Neil, Sean F; Mac, Amy; Rhodes, Gillian; Webster, Michael A
2015-12-01
Recently, we proposed that the aftereffects of adapting to facial age are consistent with a renormalization of the perceived age (e.g., so that after adapting to a younger or older age, all ages appear slightly older or younger, respectively). This conclusion has been challenged by arguing that the aftereffects can also be accounted for by an alternative model based on repulsion (in which facial ages above or below the adapting age are biased away from the adaptor). However, we show here that this challenge was based on allowing the fitted functions to take on values which are implausible and incompatible across the different adapting conditions. When the fits are constrained or interpreted in terms of standard assumptions about normalization and repulsion, then the two analyses both agree in pointing to a pattern of renormalization in age aftereffects.
Hecht, T.; Weichselbaum, A.; von Delft, J.; Bulla, R.
2008-07-01
We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows that, contrary to previous belief, NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap Δ. This allows us to calculate the impurity spectral function A(ω) very accurately for frequencies |ω|~Δ, and to resolve, in a certain parameter regime, sharp peaks in A(ω) close to the gap edge.
Energy Technology Data Exchange (ETDEWEB)
Hecht, T; Weichselbaum, A; Delft, J von [Physics Department, Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Ludwig-Maximilians-Universitaet Muenchen (Germany); Bulla, R [Theoretische Physik III, Elektronische Korrelationen und Magnetismus, Universitaet Augsburg (Germany)], E-mail: Theresa.Hecht@physik.uni-muenchen.de
2008-07-09
We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows that, contrary to previous belief, NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap {delta}. This allows us to calculate the impurity spectral function A({omega}) very accurately for frequencies |{omega}|{approx}{delta}, and to resolve, in a certain parameter regime, sharp peaks in A({omega}) close to the gap edge.
Duclut, Charlie; Delamotte, Bertrand
2017-01-01
We derive the necessary conditions for implementing a regulator that depends on both momentum and frequency in the nonperturbative renormalization-group flow equations of out-of-equilibrium statistical systems. We consider model A as a benchmark and compute its dynamical critical exponent z. This allows us to show that frequency regulators compatible with causality and the fluctuation-dissipation theorem can be devised. We show that when the principle of minimal sensitivity (PMS) is employed to optimize the critical exponents η, ν, and z, the use of frequency regulators becomes necessary to make the PMS a self-consistent criterion.
Liu, X M; Cheng, W W; Liu, J-M
2016-01-19
We investigate the quantum Fisher information and quantum phase transitions of an XY spin chain with staggered Dzyaloshinskii-Moriya interaction using the quantum renormalization-group method. The quantum Fisher information, its first-derivatives, and the finite-size scaling behaviors are rigorously calculated respectively. The singularity of the derivatives at the phase transition point as a function of lattice size is carefully discussed and it is revealed that the scaling exponent for quantum Fisher information at the critical point can be used to describe the correlation length of this model, addressing the substantial role of staggered Dzyaloshinskii-Moriya interaction in modulating quantum phase transitions.
On integrable deformations of superstring sigma models related to AdSn×Sn supercosets
Directory of Open Access Journals (Sweden)
B. Hoare
2015-08-01
Full Text Available We consider two integrable deformations of 2d sigma models on supercosets associated with AdSn×Sn. The first, the “η-deformation” (based on the Yang–Baxter sigma model, is a one-parameter generalization of the standard superstring action on AdSn×Sn, while the second, the “λ-deformation” (based on the deformed gauged WZW model, is a generalization of the non-abelian T-dual of the AdSn×Sn superstring. We show that the η-deformed model may be obtained from the λ-deformed one by a special scaling limit and analytic continuation in coordinates combined with a particular identification of the parameters of the two models. The relation between the couplings and deformation parameters is consistent with the interpretation of the first model as a real quantum deformation and the second as a root of unity quantum deformation. For the AdS2×S2 case we then explore the effect of this limit on the supergravity background associated with the λ-deformed model. We also suggest that the two models may form a dual Poisson–Lie pair and provide direct evidence for this in the case of the integrable deformations of the coset associated with S2.
Recursion relations for tree-level amplitudes in the SU(N) nonlinear sigma model
Kampf, Karol; Novotný, Jiří; Trnka, Jaroslav
2013-04-01
It is well-known that the standard Britto-Cachazo-Feng-Witten construction cannot be used for on-shell amplitudes in effective field theories due to bad behavior for large shifts. We show how to solve this problem in the case of the SU(N) nonlinear sigma model, i.e., nonrenormalizable model with an infinite number of interaction vertices, using scaling properties of the semi-on-shell currents, and we present new on-shell recursion relations for all on-shell tree-level amplitudes in this theory.
Resurgence and dynamics of O(N) and Grassmannian sigma models
2015-01-01
We study the non-perturbative dynamics of the two dimensional O ( N ) and Grassmannian sigma models by using compactification with twisted boundary conditions on ℝ × S 1 $$ \\mathbb{R}\\times {S}^1 $$ , semi-classical techniques and resurgence. While the O ( N ) model has no instantons for N > 3, it has (non-instanton) saddles on ℝ 2 $$ {\\mathbb{R}}^2 $$ , which we call 2d-saddles. On ℝ × S 1 $$ \\mathbb{R}\\times {S}^1 $$ , the resurgent relation between perturbation theory and non-perturbative ...
Dynamic Critical Behaviour of Wolff's Algorithm for $RP^N$ $\\sigma$-Models
Caracciolo, S.; Edwards, R. G.; Pelissetto, A.; Sokal, A. D.
1992-01-01
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\\sigma$-models. We find that the algorithm in which we update the embedded Ising model \\`a la Swendsen-Wang has critical slowing-down as $z_\\chi \\approx 1$. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain $z_\\chi \\approx 0$. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour ...
Application of a sigma-coordinate baroclinic model to the Baltic Sea
Directory of Open Access Journals (Sweden)
Andrzej Jankowski
2002-03-01
Full Text Available A three-dimensional (3-D sigma-coordinate baroclinic model is used to investigate water circulation and thermohaline variability in the Baltic Sea. Two versions of the horizontal resolution of ~ 10 km and ~ 5 km with 24 sigma-levels in the vertical are considered. The model is based on the Princeton Ocean Model code of Blumberg & Mellor (1987 and Mellor (1993, known as POM. This paper presents details of simulation strategies and briefly discusses the 'reality' of the results of modelling. The model's capabilities of simulating the characteristic hydrographic features of the Baltic Sea were tested for 3 months (August-October 1995, a simulation related to the period of the PIDCAP'95 experiment (Pilot Study for Intensive Data Collection and Analysis and Precipitation (Isemer 1996. The model results are compared with the in situ measurements of temperature and salinity at selected hydrographic stations, collected during cruises of r/v 'Oceania' in September and October 1995. Comparison of computed and measured temperature and salinity shows that the model reproduces the vertical structure of seawater temperature and salinity in relatively good accordance with the in situ observations. The differences between the calculated and observed values of temperature and salinity are c. 1-2oC and c. 1-2 PSU, depending on the location of the hydrographic station.
Self-dual solitons in a $CPT$-odd and Lorentz-violating gauged $O(3)$ sigma model
Casana, R; Ferreira, M M; Lazar, G
2016-01-01
We have performed a complete study of self-dual configurations in a $CPT$-odd and Lorentz-violating gauged $O(3)$ nonlinear sigma model. We have consistently implemented the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism and obtained the correspondent differential first-order equations describing electrically charged self-dual configurations. The total energy and magnetic flux of the vortices, besides being proportional to the winding number, also depend explicitly on the Lorentz-violating coefficients belonging to the sigma sector. The total electrical charge is proportional to the magnetic flux such as it occurs in Chern-Simons models. The Lorentz violation in the sigma sector allows one to interpolate between Lorentz-violating versions of some sigma models: the gauged $O(3)$ sigma model and the Maxwell-Chern-Simons $O(3)$ sigma model. The Lorentz violation enhances the amplitude of the magnetic field and BPS energy density near the origin, augmenting the deviation in relation to the solutions deprived of L...
Self-dual solitons in a C P T -odd and Lorentz-violating gauged O (3 ) sigma model
Casana, R.; Farias, C. F.; Ferreira, M. M.; Lazar, G.
2016-09-01
We have performed a complete study of self-dual configurations in a C P T -odd and Lorentz-violating gauged O (3 ) nonlinear sigma model. We have consistently implemented the Bogomol'nyi-Prasad-Sommerfield (BPS) formalism and obtained the correspondent differential first-order equations describing electrically charged self-dual configurations. The total energy and magnetic flux of the vortices, besides being proportional to the winding number, also depend explicitly on the Lorentz-violating coefficients belonging to the sigma sector. The total electrical charge is proportional to the magnetic flux such as it occurs in Chern-Simons models. The Lorentz violation in the sigma sector allows one to interpolate between Lorentz-violating versions of some sigma models: the gauged O (3 ) sigma model and the Maxwell-Chern-Simons O (3 ) sigma model. The Lorentz violation enhances the amplitude of the magnetic field and BPS energy density near the origin, augmenting the deviation in relation to the solutions deprived of Lorentz violation.
Six Sigma software development
Tayntor, Christine B
2002-01-01
Since Six Sigma has had marked success in improving quality in other settings, and since the quality of software remains poor, it seems a natural evolution to apply the concepts and tools of Six Sigma to system development and the IT department. Until now however, there were no books available that applied these concepts to the system development process. Six Sigma Software Development fills this void and illustrates how Six Sigma concepts can be applied to all aspects of the evolving system development process. It includes the traditional waterfall model and in the support of legacy systems,
On the Hamiltonian integrability of the bi-Yang-Baxter sigma-model
Delduc, Francois; Magro, Marc; Vicedo, Benoit
2015-01-01
The bi-Yang-Baxter sigma-model is a certain two-parameter deformation of the principal chiral model on a real Lie group G for which the left and right G-symmetries of the latter are both replaced by Poisson-Lie symmetries. It was introduced by C. Klimcik who also recently showed it admits a Lax pair, thereby proving it is integrable at the Lagrangian level. By working in the Hamiltonian formalism and starting from an equivalent description of the model as a two-parameter deformation of the coset sigma-model on G x G / G_diag, we show that it also admits a Lax matrix whose Poisson bracket is of the standard r/s-form characterised by a twist function which we determine. A number of results immediately follow from this, including the identification of certain complex Poisson commuting Kac-Moody currents as well as an explicit description of the q-deformed symmetries of the model. Moreover, the model is also shown to fit naturally in the general scheme recently developed for constructing integrable deformations o...
Directory of Open Access Journals (Sweden)
Antonov N.V.
2016-01-01
Full Text Available We study effects of the random fluid motion on a system in a self-organized critical state. The latter is described by the continuous stochastic model proposed by Hwa and Kardar [Phys. Rev. Lett. 62: 1813 (1989]. The advecting velocity field is Gaussian, not correlated in time, with the pair correlation function of the form ∝ δ(t − t′/k⊥d-1+ξ , where k⊥ = |k⊥| and k⊥ is the component of the wave vector, perpendicular to a certain preferred direction – the d-dimensional generalization of the ensemble introduced by Avellaneda and Majda [Commun. Math. Phys. 131: 381 (1990]. Using the field theoretic renormalization group we show that, depending on the relation between the exponent ξ and the spatial dimension d, the system reveals different types of large-scale, long-time scaling behaviour, associated with the three possible fixed points of the renormalization group equations. They correspond to ordinary diffusion, to passively advected scalar field (the nonlinearity of the Hwa–Kardar model is irrelevant and to the “pure” Hwa–Kardar model (the advection is irrelevant. For the special case ξ = 2(4 − d/3 both the nonlinearity and the advection are important. The corresponding critical exponents are found exactly for all these cases.
Chiral and U(1) axial symmetry restoration in linear sigma models with two quark flavors
Michalski, S
2006-01-01
We study the restoration of chiral symmetry in linear sigma models with two quark flavors. The models taken into consideration have a U(2) x U(2) and an O(N) internal symmetry. The physical mesons of these models are sigma, pion, \\eta and a_0 where the latter two are not present in the O(N) model. Including two-loop contributions through sunset graphs we calculate the temperature behavior of the order parameter and the masses for explicit chiral symmetry breaking with and without a U(1) axial anomaly. Decay threshold effects introduced by the sunset graphs alter the temperature dependence of the condensate and consequently that of the masses as well. Chiral symmetry tends to be restored at higher temperatures in the two-loop approximation than in the Hartree-Fock approximation. To model a dynamical restoration of the U(1) axial symmetry we imply a temperature-dependent anomaly parameter that sharply drops at about 175 MeV. This triggers the restoration of chiral symmetry before the full symmetry is restored a...
Scalar mesons in a linear sigma model with (axial-)vector mesons
Parganlija, D; Wolf, Gy; Giacosa, F; Rischke, D H
2012-01-01
The structure of the scalar mesons has been a subject of debate for many decades. In this work we look for $\\bar{q}q$ states among the physical resonances using an extended Linear Sigma Model that contains scalar, pseudoscalar, vector, and axial-vector mesons both in the non-strange and strange sectors. We perform global fits of meson masses, decay widths and amplitudes in order to ascertain whether the scalar $\\bar{q}q$ states are below or above 1 GeV. We find the scalar states above 1 GeV to be preferred as $\\bar{q}q$ states.
Directory of Open Access Journals (Sweden)
M. Abu-Shady
2014-01-01
Full Text Available A baryonic chemical potential (μb is included in the linear sigma model at finite temperature. The effective mesonic potential is numerically calculated using the N-midpoint rule. The meson masses are investigated as functions of the temperature (T at fixed value of baryonic chemical potential. The pressure and energy density are investigated as functions of temperature at fi xed value of μb. The obtained results are in good agreement in comparison with other techniques. We conclude that the calculated effective potential successfully predicts the meson properties and thermodynamic properties at finite baryonic chemical potential.
Chiral Phase Transition at Finite Isospin Density in Linear Sigma Model
Institute of Scientific and Technical Information of China (English)
SHU Song; LI Jia-Rong
2005-01-01
Using the linear sigma model, we have introduced the pion isospin chemical potential. The chiral phase transition is studied at finite temperatures and finite isospin densities. We have studied the μ - T phase diagram for the chiral phase transition and found the transition cannot happen below a certain low temperature because of the BoseEinstein condensation in this system. Above that temperature, the chiral phase transition is studied by the isotherms of pressure versus density. We indicate that the transition, in the chiral limit, is a first-order transition from a low-density phase to a high-density phase like a gas-liquid phase transition.
Finite Temperature Induced Fermion Number In The Nonlinear sigma Model In (2+1) Dimensions
Dunne, G V; Rao, K; Dunne, Gerald V.; Lopez-Sarrion, Justo; Rao, Kumar
2002-01-01
We compute the finite temperature induced fermion number for fermions coupled to a static nonlinear sigma model background in (2+1) dimensions, in the derivative expansion limit. While the zero temperature induced fermion number is well known to be topological (it is the winding number of the background), at finite temperature there is a temperature dependent correction that is nontopological -- this finite T correction is sensitive to the detailed shape of the background. At low temperature we resum the derivative expansion to all orders, and we consider explicit forms of the background as a CP^1 instanton or as a baby skyrmion.
Delta isobars in relativistic mean-field models with $\\sigma$-scaled hadron masses and couplings
Kolomeitsev, E E; Voskresensky, D N
2016-01-01
We extend the relativistic mean-field models with hadron masses and meson-baryon coupling constants dependent on the scalar $\\sigma$ field, studied previously to incorporate $\\Delta(1232)$ baryons. Available empirical information is analyzed to put constraints on the couplings of $\\Delta$s with meson fields. Conditions for the appearance of $\\Delta$s are studied. We demonstrate that with inclusion of the $\\Delta$s our equations of state continue to fulfill majority of known empirical constraints including the pressure-density constraint from heavy-ion collisions, the constraint on the maximum mass of the neutron stars, the direct Urca and the gravitational-baryon mass ratio constraints.
Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory - II
Tan, Meng-Chwan
2008-01-01
We extend our analysis in [arXiv:0801.4782] and show that the chiral algebras of (0,2) sigma models are totally trivialized by worldsheet instantons for all complete flag manifolds of compact semisimple Lie groups. Consequently, supersymmetry is spontaneously broken. Our results verify Stolz's idea that there are no harmonic spinors on the loop spaces of these flag manifolds. Moreover, they also imply that the kernels of certain twisted Dirac operators on these spaces will be empty under a "quantum" deformation of their geometries.
Non-Abelian (2,0)-super-Yang-Mills coupled to linear {sigma}-models
Energy Technology Data Exchange (ETDEWEB)
Goes-Negrao, M.S.; Helayel-Neto, J.A.; Negrao, M.R. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Universidade Catolica de Petropolis, RJ (Brazil). E-mail: negrao@cbpf.br; helayel@cbpf.br; guida@cbpf.br
2000-06-01
Considering a class of (2,0)-super-Yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here non-Abelian coupling to ordinary matter and to non-linear {sigma}-models in (2,0)-superspace. The dynamics and the couplings of the gauge potentials are discussed and the interesting feature that comes out is a sort of chirality for one of the gauge potentials whenever light-cone coordinates are chosen. (author)
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Energy Technology Data Exchange (ETDEWEB)
Tseytlin, A.A.; Wulff, L. [Blackett Laboratory, Imperial College,London SW7 2AZ (United Kingdom)
2016-06-29
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X{sub a} and imply the one-loop scale invariance of the GS sigma model. In the special case when X{sub a} is the gradient of a scalar ϕ (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in http://arxiv.org/abs/1511.05795. These equations depend on two vectors X{sub a} and K{sub a} subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X{sub a}=X{sub a}+K{sub a}). In the special case of K{sub a}=0 one finds that X{sub a}=∂{sub a}ϕ and thus obtains the standard type II supergravity equations. New generalized solutions are found if K{sub a} is chosen to be a Killing vector (and thus they exist only if the metric admits an isometry). Non-trivial solutions of the generalized equations describe K-isometric backgrounds that can be mapped by T-duality to type II supergravity solutions with dilaton containing a linear isometry-breaking term. Examples of such backgrounds appeared recently in the context of integrable η-deformations of AdS{sub n}×S{sup n} sigma models. The classical kappa-symmetry thus does not, in general, imply the 2d Weyl invariance conditions for the GS sigma model (equivalent to type II supergravity equations) but only weaker scale invariance type conditions.
Leading Logarithms in the Massive O(N) Nonlinear Sigma Model
Bijnens, Johan
2009-01-01
We review Buchler and Colangelo's result that leading divergences at any loop order can be calculated using only one-loop calculations and we provide an alternative proof. We then use this method to calculate the leading divergences of and thus the leading logarithmic corrections to the meson mass in the massive O(N) nonlinear sigma model to five-loop order. We also calculate the all-loop result to leading order in the large $N$ expansion by showing that only cactus diagrams contribute and by summing these via a generalized gap equation.
SIGMA-COORDINATE NUMERICAL MODEL FOR SIDE-DISCHARGE INTO NATURAL RIVERS
Institute of Scientific and Technical Information of China (English)
LIU Zhao-wei; CHEN Yong-can; LI Ling; ZHENG Jing-yun
2009-01-01
Due to large topography slopes in natural rivers, pollutant concentration embodies a property of three-dimensional distribution when wastewater is discharged from effluents along the bank. With the sigma coordinate along the vertical dimension fitted to both the moving free surface and the bed topography, a three-dimensional numerical model was developed in the present work to address pollutant transport processes in the above-mentioned cases. To avoid the reduction in accuracy caused by spurious diffusion in the case of steep bottom slopes, a formula for horizontal diffusion in the sigma coordinate system was derived. A case study for the side discharge into a straight open-channel flow shows that numerical results are verified well by experimental data. Furthermore, the present model is also verified by the simulation of discharging wastewater from Fuling Phosphorus Factory effluent into the Three Gorges Reservoir and the agreement between the numerical simulation results and field observation data is satisfactory. The change of the mixing zone scope in the water surface versus the layers along the vertical dimension was also discussed in detail. The study shows that a more realistic calculation for pollutant discharge has been provided by the present model than by the depth-average model which predicts an unrealistically smaller mixing zone.
Complex networks renormalization: flows and fixed points.
Radicchi, Filippo; Ramasco, José J; Barrat, Alain; Fortunato, Santo
2008-10-03
Recently, it has been claimed that some complex networks are self-similar under a convenient renormalization procedure. We present a general method to study renormalization flows in graphs. We find that the behavior of some variables under renormalization, such as the maximum number of connections of a node, obeys simple scaling laws, characterized by critical exponents. This is true for any class of graphs, from random to scale-free networks, from lattices to hierarchical graphs. Therefore, renormalization flows for graphs are similar as in the renormalization of spin systems. An analysis of classic renormalization for percolation and the Ising model on the lattice confirms this analogy. Critical exponents and scaling functions can be used to classify graphs in universality classes, and to uncover similarities between graphs that are inaccessible to a standard analysis.
Bound states of the $\\phi^4$ model via the Non-Perturbative Renormalization Group
Rose, F; Leonard, F; Delamotte, B
2016-01-01
Using the nonperturbative renormalization group, we study the existence of bound states in the symmetry-broken phase of the scalar $\\phi^4$ theory in all dimensions between two and four and as a function of the temperature. The accurate description of the momentum dependence of the two-point function, required to get the spectrum of the theory, is provided by means of the Blaizot--M\\'endez-Galain--Wschebor approximation scheme. We confirm the existence of a bound state in dimension three, with a mass within 1% of previous Monte-Carlo and numerical diagonalization values.
Entanglement Entropy in the $\\sigma$-Model with the de Sitter Target Space
Vancea, Ion V
2016-01-01
We derive the formula of the entanglement entropy between the left and right oscillating modes of the $\\sigma$-model with the de Sitter target space. To this end, we study the theory in the cosmological gauge in which the non-vanishing components of the metric on the two-dimensional base space are functions of the expansion parameter of the de Sitter space. The model is embedded in the causal north pole diamond of the Penrose diagram. We argue that the cosmological gauge is natural to the $\\sigma$-model as it is compatible with the canonical quantization relations. In this gauge, we obtain a new general solution to the equations of motion in terms of time-independent oscillating modes. The constraint structure is adequate for quantization in the Gupta-Bleuler formalism. We construct the space of states as a one-parameter family of Hilbert spaces and give the Bargmann-Fock and Jordan-Schwinger representations of it. Also, we give a simple description of the physical subspace as an infinite product of $\\mathcal...
Dynamic renormalization in the framework of nonequilibrium thermodynamics.
Ottinger, Hans Christian
2009-02-01
We show how the dynamic renormalization of nonequilibrium systems can be carried out within the general framework of nonequilibrium thermodynamics. Whereas the renormalization of Hamiltonians is well known from equilibrium thermodynamics, the renormalization of dissipative brackets, or friction matrices, is the main new feature for nonequilibrium systems. Renormalization is a reduction rather than a coarse-graining technique; that is, no new dissipative processes arise in the dynamic renormalization procedure. The general ideas are illustrated for dilute polymer solutions where, in renormalizing bead-spring chain models, dissipative hydrodynamic interactions between different smaller beads contribute to the friction coefficient of a single larger bead.
SEMICONDUCTOR INTEGRATED CIRCUITS: Sigma-delta modulator modeling analysis and design
Binjie, Ge; Xin'an, Wang; Xing, Zhang; Xiaoxing, Feng; Qingqin, Wang
2010-09-01
This paper introduces a new method for SC sigma-delta modulator modeling. It studies the integrator's different equivalent circuits in the integrating and sampling phases. This model uses the OP-AMP input pair's tail current (I0) and overdrive voltage (von) as variables. The modulator's static and dynamic errors are analyzed. A group of optimized I0 and von for maximum SNR and power × area ratio can be obtained through this model. As examples, a MASH21 modulator for digital audio and a second order modulator for RFID baseband are implemented and tested, and they can achieve 91 dB and 72 dB respectively, which verifies the modeling and design criteria.
Kappa-symmetry of superstring sigma model and generalized 10d supergravity equations
Wulff, L
2016-01-01
We determine the constraints imposed on the 10d target superspace geometry by the requirement of classical kappa-symmetry of the Green-Schwarz superstring. In the type I case we find that the background must satisfy a generalization of type I supergravity equations. These equations depend on an arbitrary vector X_a and imply the one-loop scale invariance of the GS sigma model. In the special case when X_a is the gradient of a scalar \\phi (dilaton) one recovers the standard type I equations equivalent to the 2d Weyl invariance conditions of the superstring sigma model. In the type II case we find a generalized version of the 10d supergravity equations the bosonic part of which was introduced in arXiv:1511.05795. These equations depend on two vectors \\X_a and K_a subject to 1st order differential relations (with the equations in the NS-NS sector depending only on the combination X_a = \\X_a + K_a). In the special case of K_a=0 one finds that \\X_a=\\d_a \\phi and thus obtains the standard type II supergravity equat...
Extended supersymmetric sigma models in AdS_4 from projective superspace
Butter, Daniel; Lindstrom, Ulf; Tartaglino-Mazzucchelli, Gabriele
2012-01-01
There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) in terms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdS projective-superspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the N=2 supersymmetric sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of N=1 AdS auxiliary superfields and performing a superfield duality transformation. We al...
Deformations of $T^{1,1}$ as Yang-Baxter sigma models
Crichigno, P Marcos; Yoshida, Kentaroh
2014-01-01
We consider a family of deformations of T^{1,1} in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T^{1,1}, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric. Next, we consider three-parameter deformations of T^{1,1} by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case. It is worth noting that for AdS_5 x T^{1,1}, classical integrability for the full sector has been argued to be lost. Hence our result indicates that the Yang-Baxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.
Deformations of T 1 ,1 as Yang-Baxter sigma models
Crichigno, P. Marcos; Matsumoto, Takuya; Yoshida, Kentaroh
2014-12-01
We consider a family of deformations of T 1,1 in the Yang-Baxter sigma model approach. We first discuss a supercoset description of T 1,1, which makes manifest the full symmetry of the space and leads to the standard Sasaki-Einstein metric. Next, we consider three-parameter deformations of T 1,1 by using classical r-matrices satisfying the classical Yang-Baxter equation (CYBE). The resulting metric and NS-NS two-form agree exactly with the ones obtained via TsT transformations, and contain the Lunin-Maldacena background as a special case. It is worth noting that for AdS5 × T 1,1 , classical integrability for the full sector has been argued to be lost. Hence our result indicates that the Yang-Baxter sigma model approach is applicable even for non-integrable cosets. This observation suggests that the gravity/CYBE correspondence can be extended beyond integrable cases.
Uccellini, L. W.; Johnson, D. R.; Schlesinger, R. E.
1979-01-01
A solution is presented for matching boundary conditions across the interface of an isentropic and sigma coordinate hybrid model. A hybrid model based on the flux form of the primitive equations is developed which allows direct vertical exchange between the model domains, satisfies conservation principles with respect to transport processes, and maintains a smooth transition across the interface without need for artificial adjustment or parameterization schemes. The initial hybrid model simulations of a jet streak propagating in a zonal channel are used to test the feasibility of the hybrid model approach. High efficiency of the hybrid model is demonstrated.
Antonov, N V; Gulitskiy, N M
2012-06-01
The field theoretic renormalization group and operator product expansion are applied to the Kazantsev-Kraichnan kinematic model for the magnetohydrodynamic turbulence. The anomalous scaling emerges as a consequence of the existence of certain composite fields ("operators") with negative dimensions. The anomalous exponents for the correlation functions of arbitrary order are calculated in the two-loop approximation (second order of the renormalization-group expansion), including the anisotropic sectors. The anomalous scaling and the hierarchy of anisotropic contributions become stronger due to those second-order contributions.
Fermion field renormalization prescriptions
Zhou, Yong
2005-01-01
We discuss all possible fermion field renormalization prescriptions in conventional field renormalization meaning and mainly pay attention to the imaginary part of unstable fermion Field Renormalization Constants (FRC). We find that introducing the off-diagonal fermion FRC leads to the decay widths of physical processes $t\\to c Z$ and $b\\to s \\gamma$ gauge-parameter dependent. We also discuss the necessity of renormalizing the bare fields in conventional quantum field theory.
S-Matrices and Quantum Group Symmetry of q-Deformed Sigma Models
Hollowood, Timothy J; Schmidtt, David M
2015-01-01
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the q-deformations with q a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
S-matrices and quantum group symmetry of k-deformed sigma models
Hollowood, Timothy J.; Miramontes, J. Luis; Schmidtt, David M.
2016-11-01
Recently, two kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed (Delduc et al 2014 Phys. Rev. Lett. 112 051601; Hollowood et al 2014 J. Phys. A: Math. Theor. 47 495402). One class of these, the k deformations associated to the more general q deformations but with q={{{e}}}{{i}π /k} a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum group symmetry.
Topological self-dual configurations in a Lorentz-violating gauged O (3 ) sigma model
Casana, R.; Farias, C. F.; Ferreira, M. M.
2015-12-01
We have studied the existence of topological Bogomol'nyi-Prasad-Sommerfield or self-dual configurations in a Lorentz-violating gauged O (3 ) nonlinear sigma model, where C P T -even Lorentz-violating (LV) terms were introduced in both the gauge and σ -field sectors. As happens in the usual gauged σ model, purely magnetic self-dual configurations are allowed, maintaining some qualitative features of the standard ones. In a more involved configuration, Lorentz violation provides new self-dual magnetic solutions carrying an electric field but a null total electric charge. In both cases, the total energy of the self-dual configurations turns out to be proportional to the topological charge of the model and to the LV parameters introduced in the σ sector. It is shown that the LV terms yield magnetic flux reversion as well.
Twining Genera of (0,4) Supersymmetric Sigma Models on K3
Harrison, Sarah; Paquette, Natalie M
2013-01-01
Conformal field theories with (0,4) worldsheet supersymmetry and K3 target can be used to compactify the E8xE8 heterotic string to six dimensions in a supersymmetric manner. The data specifying such a model includes an appropriate configuration of 24 gauge instantons in the E8xE8 gauge group to satisfy the constraints of anomaly cancellation. In this note, we compute twining genera - elliptic genera with appropriate insertions of discrete symmetry generators in the trace - for (0,4) theories with various instanton embeddings. We do this by constructing linear sigma models which flow to the desired conformal field theories, and using the techniques of localization. We present several examples of such twining genera which are consistent with a moonshine relating these (0,4) models to the finite simple sporadic group M24.
Simulating the All-Order Strong Coupling Expansion III: O(N) sigma/loop models
Wolff, Ulli
2009-01-01
We reformulate the O(N) sigma model as a loop model whose configurations are the all-order strong coupling graphs of the original model. The loop configurations are represented by a pointer list in the computer and a Monte Carlo update scheme is proposed. Sample simulations are reported and the method turns out to be similarly efficient as the reflection cluster method, but it has greater potential for systematic generalization to other lattice field theories. A variant action suggested by the method is also simulated and leads to a rather extreme demonstration of the concept of universality of the scaling or continuum limit. {\\it I would like to dedicate this paper to Martin L\\"uscher on the occasion of his sixtieth birthday. I thank him for his superb contributions to quantum field theory and for the privilege to collaborate with him.}
The scaling region of the lattice O(N) sigma model at finite temperature
Strouthos, C G; Strouthos, Costas G.; Tziligakis, Ioannis N.
2003-01-01
We present results from numerical studies of the finite temperature phase transition of the $(3+1)d$ O(N)-symmetric non-linear sigma model for $N=1,2$ and 3. We study the dependence of the width of the 3d critical region on $N$ and we show that the broken phase scaling region is much wider for N=1 and 2 than for N=1. We compare the widths of the critical region in the low $T$ and high $T$ phases of the O(2) model and we show that the scaling region in the broken phase is much wider than in the symmetric phase. We also report results for the width of the scaling region in the low $T$ phase $(2+1)d$ Ising model and we show that the spatial correlation length has to be approximately twice the lattice temporal extent before the 2d scaling region is reached.
Dynamic Critical Behaviour of Wolff's Algorithm for $RP^N$ $\\sigma$-Models
Caracciolo, Sergio; Pelissetto, A; Sokal, A D
1992-01-01
We study the performance of a Wolff-type embedding algorithm for $RP^N$ $\\sigma$-models. We find that the algorithm in which we update the embedded Ising model \\`a la Swendsen-Wang has critical slowing-down as $z_\\chi \\approx 1$. If instead we update the Ising spins with a perfect algorithm which at every iteration produces a new independent configuration, we obtain $z_\\chi \\approx 0$. This shows that the Ising embedding encodes well the collective modes of the system, and that the behaviour of the first algorithm is connected to the poor performance of the Swendsen-Wang algorithm in dealing with a frustrated Ising model.
Photon as a Vector Goldstone Boson: Nonlinear $\\sigma $ Model for QED
Chkareuli, J L; Mohapatra, Rabindra N; Nielsen, H B
2004-01-01
We show that QED in the Coulomb gauge can be considered as a low energy linear approximation of a non-linear $\\sigma $-type model where the photon emerges as a vector Goldstone boson related to the spontaneous breakdown of Lorentz symmetry down to its spatial rotation subgroup at some high scale $M$. Starting with a general massive vector field theory one naturally arrives at this model if the pure spin-1 value for the vector field $A_{\\mu }(x)$ provided by the Lorentz condition $\\partial _{\\mu }A_{\\mu }(x)=0$ is required. The model coincides with conventional QED in the Coulomb gauge in the limit of M going to infinity and generates a very particular form for the Lorentz and CPT symmetry breaking terms, which are suppressed by powers of $M$.
Quasi-Topological Gauged Sigma Models, The Geometric Langlands Program, And Knots
Tan, Meng-Chwan
2011-01-01
We construct and study a closed, two-dimensional, quasi-topological (0,2) gauged sigma model with target space a smooth G-manifold, where G is any compact and connected Lie group. When the target space is a flag manifold of simple G, and the gauge group is a Cartan subgroup thereof, the perturbative model describes, purely physically, the recently formulated mathematical theory of "Twisted Chiral Differential Operators". This paves the way, via a generalized T-duality, for a natural physical interpretation of the geometric Langlands correspondence for simply-connected, simple, complex Lie groups. In particular, the Hecke eigensheaves and Hecke operators can be described in terms of the correlation functions of certain operators that underlie the infinite-dimensional chiral algebra of the flag manifold model. Nevertheless, nonperturbative worldsheet twisted-instantons can, in some situations, trivialize the chiral algebra completely. This leads to a spontaneous breaking of supersymmetry whilst implying certain...
Hewson, Alex C; Bauer, Johannes
2010-03-24
We show that information on the probability density of local fluctuations can be obtained from a numerical renormalization group calculation of a reduced density matrix. We apply this approach to the Anderson-Holstein impurity model to calculate the ground state probability density ρ(x) for the displacement x of the local oscillator. From this density we can deduce an effective local potential for the oscillator and compare its form with that obtained from a semiclassical approximation as a function of the coupling strength. The method is extended to the infinite dimensional Holstein-Hubbard model using dynamical mean field theory. We use this approach to compare the probability densities for the displacement of the local oscillator in the normal, antiferromagnetic and charge ordered phases.
Inclusive $\\Sigma^{+}$ and $\\Sigma^{0}$ Production in Hadronic Z Decays
Acciarri, M; Adriani, O; Aguilar-Benítez, M; Alcaraz, J; Alemanni, G; Allaby, James V; Aloisio, A; Alviggi, M G; Ambrosi, G; Anderhub, H; Andreev, V P; Angelescu, T; Anselmo, F; Arefev, A; Azemoon, T; Aziz, T; Bagnaia, P; Bajo, A; Baksay, L; Balandras, A; Banerjee, S; Banerjee, Sw; Barczyk, A; Barillère, R; Barone, L; Bartalini, P; Basile, M; Battiston, R; Bay, A; Becattini, F; Becker, U; Behner, F; Bellucci, L; Berbeco, R; Berdugo, J; Berges, P; Bertucci, B; Betev, B L; Bhattacharya, S; Biasini, M; Biland, A; Blaising, J J; Blyth, S C; Bobbink, Gerjan J; Böhm, A; Boldizsar, L; Borgia, B; Bourilkov, D; Bourquin, Maurice; Braccini, S; Branson, J G; Brigljevic, V; Brochu, F; Buffini, A; Buijs, A; Burger, J D; Burger, W J; Cai, X D; Campanelli, M; Capell, M; Cara Romeo, G; Carlino, G; Cartacci, A M; Casaus, J; Castellini, G; Cavallari, F; Cavallo, N; Cecchi, C; Cerrada-Canales, M; Cesaroni, F; Chamizo-Llatas, M; Chang, Y H; Chaturvedi, U K; Chemarin, M; Chen, A; Chen, G; Chen, G M; Chen, H F; Chen, H S; Chiefari, G; Cifarelli, Luisa; Cindolo, F; Civinini, C; Clare, I; Clare, R; Coignet, G; Colijn, A P; Colino, N; Costantini, S; Cotorobai, F; Cozzoni, B; de la Cruz, B; Csilling, Akos; Cucciarelli, S; Dai, T S; van Dalen, J A; D'Alessandro, R; De Asmundis, R; Déglon, P L; Degré, A; Deiters, K; Della Volpe, D; Denes, P; De Notaristefani, F; De Salvo, A; Diemoz, M; Van Dierendonck, D N; Di Lodovico, F; Dionisi, C; Dittmar, Michael; Dominguez, A; Doria, A; Dova, M T; Duchesneau, D; Dufournaud, D; Duinker, P; Durán, I; El-Mamouni, H; Engler, A; Eppling, F J; Erné, F C; Extermann, Pierre; Fabre, M; Faccini, R; Falagán, M A; Falciano, S; Favara, A; Fay, J; Fedin, O; Felcini, Marta; Ferguson, T; Ferroni, F; Fesefeldt, H S; Fiandrini, E; Field, J H; Filthaut, Frank; Fisher, P H; Fisk, I; Forconi, G; Fredj, L; Freudenreich, Klaus; Furetta, C; Galaktionov, Yu; Ganguli, S N; García-Abia, P; Gataullin, M; Gau, S S; Gentile, S; Gheordanescu, N; Giagu, S; Gong, Z F; Grenier, G; Grimm, O; Grünewald, M W; Guida, M; van Gulik, R; Gupta, V K; Gurtu, A; Gutay, L J; Haas, D; Hasan, A; Hatzifotiadou, D; Hebbeker, T; Hervé, A; Hidas, P; Hirschfelder, J; Hofer, H; Holzner, G; Hoorani, H; Hou, S R; Hu, Y; Iashvili, I; Jin, B N; Jones, L W; de Jong, P; Josa-Mutuberria, I; Khan, R A; Kaur, M; Kienzle-Focacci, M N; Kim, D; Kim, J K; Kirkby, Jasper; Kiss, D; Kittel, E W; Klimentov, A; König, A C; Kopp, A; Koutsenko, V F; Kräber, M H; Krämer, R W; Krenz, W; Krüger, A; Kunin, A; Ladrón de Guevara, P; Laktineh, I; Landi, G; Lassila-Perini, K M; Lebeau, M; Lebedev, A; Lebrun, P; Lecomte, P; Lecoq, P; Le Coultre, P; Lee, H J; Le Goff, J M; Leiste, R; Leonardi, E; Levchenko, P M; Li Chuan; Likhoded, S A; Lin, C H; Lin, W T; Linde, Frank L; Lista, L; Liu, Z A; Lohmann, W; Longo, E; Lü, Y S; Lübelsmeyer, K; Luci, C; Luckey, D; Lugnier, L; Luminari, L; Lustermann, W; Ma Wen Gan; Maity, M; Malgeri, L; Malinin, A; Maña, C; Mangeol, D J J; Mans, J; Marchesini, P A; Marian, G; Martin, J P; Marzano, F; Massaro, G G G; Mazumdar, K; McNeil, R R; Mele, S; Merola, L; Meschini, M; Metzger, W J; Von der Mey, M; Mihul, A; Milcent, H; Mirabelli, G; Mnich, J; Mohanty, G B; Molnár, P; Monteleoni, B; Moulik, T; Muanza, G S; Muheim, F; Muijs, A J M; Musy, M; Napolitano, M; Nessi-Tedaldi, F; Newman, H; Niessen, T; Nisati, A; Nowak, H; Organtini, G; Oulianov, A; Palomares, C; Pandoulas, D; Paoletti, S; Paolucci, P; Paramatti, R; Park, H K; Park, I H; Pascale, G; Passaleva, G; Patricelli, S; Paul, T; Pauluzzi, M; Paus, C; Pauss, Felicitas; Pedace, M; Pensotti, S; Perret-Gallix, D; Petersen, B; Piccolo, D; Pierella, F; Pieri, M; Piroué, P A; Pistolesi, E; Plyaskin, V; Pohl, M; Pozhidaev, V; Postema, H; Pothier, J; Produit, N; Prokofev, D; Prokofiev, D O; Quartieri, J; Rahal-Callot, G; Rahaman, M A; Raics, P; Raja, N; Ramelli, R; Rancoita, P G; Raspereza, A V; Raven, G; Razis, P A; Ren, D; Rescigno, M; Reucroft, S; Van Rhee, T; Riemann, S; Riles, K; Robohm, A; Rodin, J; Roe, B P; Romero, L; Rosca, A; Rosier-Lees, S; Rubio, Juan Antonio; Ruschmeier, D; Rykaczewski, H; Saremi, S; Sarkar, S; Salicio, J; Sánchez, E; Sanders, M P; Sarakinos, M E; Schäfer, C; Shchegelskii, V; Schmidt-Kärst, S; Schmitz, D; Schopper, Herwig Franz; Schotanus, D J; Schwering, G; Sciacca, C; Sciarrino, D; Seganti, A; Servoli, L; Shevchenko, S; Shivarov, N; Shoutko, V; Shumilov, E; Shvorob, A V; Siedenburg, T; Son, D; Smith, B; Spillantini, P; Steuer, M; Stickland, D P; Stone, A; Stone, H; Stoyanov, B; Strässner, A; Sudhakar, K; Sultanov, G G; Sun, L Z; Suter, H; Swain, J D; Szillási, Z; Sztaricskai, T; Tang, X W; Tauscher, Ludwig; Taylor, L; Tellili, B; Timmermans, C; Ting, Samuel C C; Ting, S M; Tonwar, S C; Tóth, J; Tully, C; Tung, K L; Uchida, Y; Ulbricht, J; Valente, E; Vesztergombi, G; Vetlitskii, I; Vicinanza, D; Viertel, Gert M; Villa, S; Vivargent, M; Vlachos, S; Vodopyanov, I; Vogel, H; Vogt, H; Vorobev, I; Vorobyov, A A; Vorvolakos, A; Wadhwa, M; Wallraff, W; Wang, M; Wang, X L; Wang, Z M; Weber, A; Weber, M; Wienemann, P; Wilkens, H; Wu, S X; Wynhoff, S; Xia, L; Xu, Z Z; Yamamoto, J; Yang, B Z; Yang, C G; Yang, H J; Yang, M; Ye, J B; Yeh, S C; Zalite, A; Zalite, Yu; Zhang, Z P; Zhu, G Y; Zhu, R Y; Zichichi, A; Zilizi, G; Zöller, M
2000-01-01
We report on measurements of the inclusive production rate of $\\Sigma^+$ and $\\Sigma^0$ baryons in hadronic Z decays collected with the L3 detector at LEP. The $\\Sigma^+$ baryons are detected through the decay $\\Sigma^+ \\rightarrow {\\rm p} \\pi^0$, while the $\\Sigma^0$ baryons are detected via the decay mode $\\Sigma^0 \\rightarrow \\Lambda \\gamma$. The average numbers of $\\Sigma^+$ and $\\Sigma^0$ per hadronic Z decay are measured to be: \\begin{eqnarray*} \\left + \\left & = & 0.114 \\pm 0.011_{\\mbox{\\it \\small stat}} \\pm 0.009_{\\mbox{\\it \\small syst}} \\\\ \\left + \\left & = & 0.095 \\pm 0.015_{\\mbox{\\it \\small stat}} \\pm 0.013_{\\mbox{\\it \\small syst}} \\ \\mbox{.} \\end{eqnarray*} These rates are found to be higher than the predictions from Monte Carlo hadronization models and analytical parameterizations of strange baryon production.
Renormalization: an advanced overview
Gurau, R.; Rivasseau, V.; Sfondrini, A.|info:eu-repo/dai/nl/330983083
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond
Renormalized action improvements
Energy Technology Data Exchange (ETDEWEB)
Zachos, C.
1984-01-01
Finite lattice spacing artifacts are suppressed on the renormalized actions. The renormalized action trajectories of SU(N) lattice gauge theories are considered from the standpoint of the Migdal-Kadanoff approximation. The minor renormalized trajectories which involve representations invariant under the center are discussed and quantified. 17 references.
Higher spin holography and the AdS string sigma model
Polyakov, Dimitri
2013-05-01
We analyse the cubic spin-3 interaction in AdS space using the higher spin extension of the string-theoretic sigma-model constructed in our previous work, whose low energy limit is described by the AdS vacuum solution. We find that, in the leading order of the cosmological constant, the spin-3 correlator on the AdS4 string theory side reproduces the structure of the three-point function of composite operators, quadratic in free fields, in the dual d = 3 vector model. The cancellation of holography violating terms in d = 3 is related to the value of the Liouville background charge in d = 4. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.
Decays of open charmed mesons in the extended Linear Sigma Model
Directory of Open Access Journals (Sweden)
Eshraim Walaa I.
2014-01-01
Full Text Available We enlarge the so-called extended linear Sigma model (eLSM by including the charm quark according to the global U(4r × U(4l chiral symmetry. In the eLSM, besides scalar and pseudoscalar mesons, also vector and axial-vector mesons are present. Almost all the parameters of the model were fixed in a previous study of mesons below 2 GeV. In the extension to the four-flavor case, only three additional parameters (all of them related to the bare mass of the charm quark appear.We compute the (OZI dominant strong decays of open charmed mesons. The results are compatible with the experimental data, although the theoretical uncertainties are still large.
Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
Directory of Open Access Journals (Sweden)
Andrea Quadri
2014-04-01
Full Text Available We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE encoding the invariance of the SU(2 Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI amplitudes (both on-shell and off-shell can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed.
The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement
Liebling, S L
2002-01-01
Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is known to have two regimes, one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.
Two-loop renormalization of fermion bilinear operators on the lattice
Skouroupathis, A
2010-01-01
We compute the renormalization functions on the lattice, in the RI' scheme, of local bilinear quark operators $\\bar{\\psi}\\Gamma\\psi$, where $\\Gamma= 1, \\gamma_5, \\gamma_\\mu, \\gamma_5\\gamma_\\mu, \\gamma_5\\sigma_{\\mu\
Cook, Paul P
2016-01-01
We investigate two-parameter solutions of sigma-models on two dimensional symmetric spaces contained in E11. Embedding such sigma-model solutions in space-time gives solutions of M* and M'-theory where the metric depends on general travelling wave functions, as opposed to harmonic functions typical in general relativity, supergravity and M-theory. Weyl reflection allows such solutions to be mapped to M-theory solutions where the wave functions depend explicitly on extra coordinates contained in the fundamental representation of E11.
Pierce, R. B.; Johnson, Donald R.; Reames, Fred M.; Zapotocny, Tom H.; Wolf, Bart J.
1991-01-01
The normal-mode characteristics of baroclinically amplifying disturbances were numerically investigated in a series of adiabatic simulations by a hybrid isentropic-sigma model, demonstrating the effect of coupling an isentropic-coordinate free atmospheric domain with a sigma-coordinate PBL on the normal-mode characteristics. Next, the normal-mode model was modified by including a transport equation for water vapor and adiabatic heating by condensation. Simulations with and without a hydrological component showed that the overall effect of latent heat release is to markedly enhance cyclogenesis and frontogenesis.
Wu, Yue-Liang
2014-04-01
To understand better the quantum structure of field theory and standard model in particle physics, it is necessary to investigate carefully the divergence structure in quantum field theories (QFTs) and work out a consistent framework to avoid infinities. The divergence has got us into trouble since developing quantum electrodynamics in 1930s. Its treatment via the renormalization scheme is satisfied not by all physicists, like Dirac and Feynman who have made serious criticisms. The renormalization group analysis reveals that QFTs can in general be defined fundamentally with the meaningful energy scale that has some physical significance, which motivates us to develop a new symmetry-preserving and infinity-free regularization scheme called loop regularization (LORE). A simple regularization prescription in LORE is realized based on a manifest postulation that a loop divergence with a power counting dimension larger than or equal to the space-time dimension must vanish. The LORE method is achieved without modifying original theory and leads the divergent Feynman loop integrals well-defined to maintain the divergence structure and meanwhile preserve basic symmetries of original theory. The crucial point in LORE is the presence of two intrinsic energy scales which play the roles of ultraviolet cutoff Mc and infrared cutoff μs to avoid infinities. As Mc can be made finite when taking appropriately both the primary regulator mass and number to be infinity to recover the original integrals, the two energy scales Mc and μs in LORE become physically meaningful as the characteristic energy scale and sliding energy scale, respectively. The key concept in LORE is the introduction of irreducible loop integrals (ILIs) on which the regularization prescription acts, which leads to a set of gauge invariance consistency conditions between the regularized tensor-type and scalar-type ILIs. An interesting observation in LORE is that the evaluation of ILIs with ultraviolet
On non-minimal N = 4 supermultiplets in 1D and their associated {sigma}-models
Energy Technology Data Exchange (ETDEWEB)
Gonzales, Marcelo; Khodaee, Sadi; Toppan, Francesco, E-mail: marcbino@cbpf.b, E-mail: khodaee@cbpf.b, E-mail: toppan@cbpf.b
2010-10-15
We construct the non-minimal linear representations of the N = 4 Extended Supersymmetry in one-dimension. They act on 8 bosonic and 8 fermionic fields. Inequivalent representations are specified by the mass-dimension of the fields and the connectivity of the associated graphs. The oxidation to minimal N = 5 linear representations is given. Two types of N = 4 {sigma}-models based on non-minimal representations are obtained: the resulting off-shell actions are either manifestly invariant or depend on a constrained pre potential. The connectivity properties of the graphs play a decisive role in discriminating inequivalent actions. These results find application in partial breaking of supersymmetric theories. (author)
Measuring the Topological Susceptibility in a Fixed Sector: Results for Sigma Models
Bautista, Irais; Dromard, Arthur; Gerber, Urs; Hofmann, Christoph P; Mejía-Díaz, Héctor; Wagner, Marc
2015-01-01
For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( - ^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models yield accurate results for chi_t, which confirm that the method is applicable. Unfortunately, for increasing volume the wanted signal gets rapidly suppressed, and this method requires huge statistics.
Institute of Scientific and Technical Information of China (English)
ZHU Shouxian; ZHANG Wenjing
2008-01-01
Much has been written of the error in computing the baroclinic pressure gradient (BPG) with sigma coordinates in ocean or atmos- pheric numerical models. The usual way to reduce the error is to subtract area-averaged density stratification of the whole computa- tion region. But if there is great difference between the area-averaged and the local averaged density stratification, the error will be obvious. An example is given to show that the error from this method may be larger than that from no correction sometimes. The definition of local area is put forward. Then, four improved BPG difference schemes of subtracting the local averaged density strat- ification are designed to reduce the error. Two of them are for diagnostic calculation (density field is fixed), and the others are for prognostic calculation (density field is not fixed). The results show that the errors from these schemes all significantly decrease.
Wen, D; Wang, X; Ai, B; Liu, G; Dong, D; Liu, L; Wen, De-hua; Chen, Wei; Wang, Xian-ju; Ai, Bao-quan; Liu, Guo-tao; Dong, Dong-qiao; Liu, Liang-gang
2003-01-01
The influence of the rotation on the total masses and radii of the neutron stars are calculated by the Hartle's slow rotation formalism, while the equation of state is considered in a relativistic $\\sigma-\\omega$ model. Comparing with the observation, the calculating result shows that the double neutron star binaries are more like hyperon stars and the neutron stars of X-ray binaries are more like traditional neutron stars. As the changes of the mass and radius to a real neutron star caused by the rotation are very small comparing with the total mass and radius, one can see that Hartle's approximate method is rational to deal with the rotating neutron stars. If three property values: mass, radius and period are observed to the same neutron star, then the EOS of this neutron star could be decided entirely.
Ramalho, G
2012-01-01
We study the $\\gamma^\\ast \\Lambda \\to \\Sigma^0$ transition form factors by applying the covariant spectator quark model. Using the parametrization for the baryon core wave functions as well as for the pion cloud dressing obtained in a previous work, we calculate the dependence on the momentum transfer squared, $Q^2$, of the electromagnetic transition form factors. The magnetic form factor is dominated by the valence quark contributions. The final result for the transition magnetic moment, a combination of the quark core and pion cloud effects, turns out to give a value very close to the data. The pion cloud, although small, makes the result towards the data. It is also predicted that small but nonzero values for the electric form factor in the finite $Q^2$ region, as a consequence of the pion cloud dressing.
Huang, Z; Huang, Zheng; Suzuki, Mahiko
1996-01-01
We obtain the general analytic solutions of the nonlinear \\sigma-model in 3+1 dimensions as the candidates for the disoriented chiral condensate (DCC). The nonuniformly isospin-orientated solutions are shown to be related to the uniformly oriented ones through the chiral (axial) rotations. We discuss the pion charge distribution arising from these solutions. The distribution dP/df=1/(2\\sqrt{f}) holds for the uniform solutions in general and the nonuniform solutions in the 1+1 boost invariant case. For the nonuniform solution in 1+1 without a boost-invariance and in higher dimensions, the distribution does not hold in the integrated form. However, it is applicable to the pions selected from a small segment in the momentum phase space. We suggest that the nonuniform DCC's may correspond to the mini-Centauro events.
Loop formulation of the supersymmetric nonlinear O(N) sigma model
Steinhauer, Kyle
2013-01-01
We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For $N \\ge 3$ this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For $N=2$ we determine the critical point and present boson and fermion masses in the critical regime.
Apparently non-invariant terms of nonlinear sigma models in lattice perturbation theory
Harada, Koji; Kubo, Hirofumi; Yamamoto, Yuki
2009-01-01
Apparently non-invariant terms (ANTs) which appear in loop diagrams for nonlinear sigma models (NLSs) are revisited in lattice perturbation theory. The calculations have been done mostly with dimensional regularization so far. In order to establish that the existence of ANTs is independent of the regularization scheme, and of the potential ambiguities in the definition of the Jacobian of the change of integration variables from group elements to "pion" fields, we employ lattice regularization, in which everything (including the Jacobian) is well-defined. We show explicitly that lattice perturbation theory produces ANTs in the four-point functions of the "pion" fields at one-loop and the Jacobian does not play an important role in generating ANTs.
Radiative decays of light vector mesons in a quark level linear sigma model
Napsuciale, M; Alvarado-Anell, E
2003-01-01
We calculate the P0 to gamma gamma, V0 to P0 gamma and V0to V'0 gamma gamma decays in the framework of a U(3)xU(3) linear sigma model which includes constituent quarks. For the first two decays this approach improves results based on the anomalous Wess-Zumino term, with contributions due to SU(3) symmetry breaking and vector mixing. The phi to (omega,rho) gamma gamma decays are dominated by resonant eta' exchange . Our calculation for the later decays improves and update similar calculations in the -closely related- framework of vector meson dominance. We obtain BR(phi to rho gamma gamma)=2.5x10^{-5} and BR(phi to omega gamma gamma)=2.8x10^{-6} within the scope of the high-luminosity phi factories.
Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
Gonzales, Marcelo; Khodaee, Sadi; Toppan, Francesco
2012-01-01
"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs are known as "Adinkras"). We further prove the existence of "entangled" linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3,8,5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as chirality and coloring can discriminate different supermultiplets. The tools used in our classification have been previously introduced and discu...
Algebraic Structure of tt * Equations for Calabi-Yau Sigma Models
Alim, Murad
2017-08-01
The tt * equations define a flat connection on the moduli spaces of {2d, \\mathcal{N}=2} quantum field theories. For conformal theories with c = 3 d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. We show that the non-holomorphic content of the tt * equations, restricted to the conformal directions, in the cases d = 1, 2, 3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space. This space parameterizes a freedom in choosing representatives of the chiral ring while preserving a constant topological metric. Geometrically, the freedom corresponds to a choice of forms on the target space respecting the Hodge filtration and having a constant pairing. Linear combinations of vector fields on that space are identified with the generators of a Lie algebra. This Lie algebra replaces the non-holomorphic derivatives of tt * and provides these with a finer and algebraic meaning. For sigma models into lattice polarized K3 manifolds, the differential ring of special functions on the moduli space is constructed, extending known structures for d = 1 and 3. The generators of the differential rings of special functions are given by quasi-modular forms for d = 1 and their generalizations in d = 2, 3. Some explicit examples are worked out including the case of the mirror of the quartic in {\\mathbbm{P}^3}, where due to further algebraic constraints, the differential ring coincides with quasi modular forms.
BTZ black hole from Poisson–Lie T-dualizable sigma models with spectators
Directory of Open Access Journals (Sweden)
A. Eghbali
2017-09-01
Full Text Available The non-Abelian T-dualization of the BTZ black hole is discussed in detail by using the Poisson–Lie T-duality in the presence of spectators. We explicitly construct a dual pair of sigma models related by Poisson–Lie symmetry. The original model is built on a 2+1-dimensional manifold M≈O×G, where G as a two-dimensional real non-Abelian Lie group acts freely on M, while O is the orbit of G in M. The findings of our study show that the original model indeed is canonically equivalent to the SL(2,R Wess–Zumino–Witten (WZW model for a given value of the background parameters. Moreover, by a convenient coordinate transformation we show that this model describes a string propagating in a spacetime with the BTZ black hole metric in such a way that a new family of the solutions to low energy string theory with the BTZ black hole vacuum metric, constant dilaton field and a new torsion potential is found. The dual model is built on a 2+1-dimensional target manifold M˜ with two-dimensional real Abelian Lie group G˜ acting freely on it. We further show that the dual model yields a three-dimensional charged black string for which the mass M and axion charge Q per unit length are calculated. After that, the structure and asymptotic nature of the dual space–time including the horizon and singularity are determined.
Renormalization of a Lorentz invariant doubled worldsheet theory
Nibbelink, Stefan Groot; Patalong, Peter
2013-01-01
Manifestly T-duality covariant worldsheet string models can be constructed by doubling the coordinate fields. We describe the underlying gauge symmetry of a recently proposed Lorentz invariant doubled worldsheet theory that makes half of the worldsheet degrees of freedom redundant. By shifting the Lagrange multiplier, that enforces the gauge fixing condition, the worldsheet action can be cast into various guises. We investigate the renormalization of this theory using a non-linear background/quantum split by employing a normal coordinate expansion adapted to the gauge-fixed theory. The propagator of the doubled coordinates contains a projection operator encoding that half of them do not propagate. We determine the doubled target space equations of motion by requiring one-loop Weyl invariance. Some of them are generalizations of the conventional sigma model beta-functions, while others seem to be novel to the doubled theory: In particular, a dilaton equation seems related to the strong constraint of double fie...
Classen, Laura; Xing, Rui-Qi; Khodas, Maxim; Chubukov, Andrey V
2017-01-20
We report the results of the parquet renormalization group (RG) analysis of the phase diagram of the most general 5-pocket model for Fe-based superconductors. We use as an input the orbital structure of excitations near the five pockets made out of d_{xz}, d_{yz}, and d_{xy} orbitals and argue that there are 40 different interactions between low-energy fermions in the orbital basis. All interactions flow under the RG, as one progressively integrates out fermions with higher energies. We find that the low-energy behavior is amazingly simple, despite the large number of interactions. Namely, at low energies the full 5-pocket model effectively reduces either to a 3-pocket model made of one d_{xy} hole pocket and two electron pockets or a 4-pocket model made of two d_{xz}/d_{yz} hole pockets and two electron pockets. The leading instability in the effective 4-pocket model is a spontaneous orbital (nematic) order, followed by s^{+-} superconductivity. In the effective 3-pocket model, orbital fluctuations are weaker, and the system develops either s^{+-} superconductivity or a stripe spin-density wave. In the latter case, nematicity is induced by composite spin fluctuations.
Does \\Sigma -\\Sigma -\\alpha Form a Quasi-Bound State?
Htun Oo, H; Kamada, H; Glöckle, W
2004-01-01
We have investigated the possible existence of a quasi-bound state for the \\Sigma -\\Sigma -\\alpha system in the framework of Faddeev calculations. We are particularly interested in the state of total iso-spin T=2, since for an inert \\alpha particle there is no strong conversion to \\Xi -N-\\alpha or \\Lambda -\\Lambda -\\alpha possible. A \\Sigma -\\alpha optical potential based on Nijmegen model D and original \\Sigma -\\Sigma interactions of the series of Nijmegen potentials NSC97 as well a simulated Gaussian type versions thereof are used. Our investigation of the \\Sigma -\\Sigma -\\alpha system leads to a quasi bound state where, depending on the potential parameters, the energy ranges between -1.4 and -2.4 MeV and the level width is about 0.2MeV.
Running Head: Implementing Six Sigma Efforts
Lindsay, Jamie Eleaitia Mae
2005-01-01
Six Sigma is an organization wide program that provides common set of goals, language, and methodology for improving the overall quality of the processes within the organization (Davis & Heineke 2004). Six Sigma main concern is for the customer. What will the customers want? Need? Six Sigma has a model that helps Sigma get implemented DMAIC model…
Large-N Solution of the Heterotic Weighted Non-Linear Sigma-Model
Koroteev, Peter; Vinci, Walter
2010-01-01
We study a heterotic two-dimensional N=(0,2) gauged non-linear sigma-model whose target space is a weighted complex projective space. We consider the case with N positively and \\tilde{N}=N_F - N negatively charged fields. This model is believed to give a description of the low-energy physics of a non-Abelian semi-local vortex in a four-dimensional N=2 supersymmetric U(N) gauge theory with N_F > N matter hypermultiplets. The supersymmetry in the latter theory is broken down to N=1 by a mass term for the adjoint fields. We solve the model in the large-N approximation and explore a two-dimensional subset of the mass parameter space for which a discrete Z_{N-\\tilde{N}} symmetry is preserved. Supersymmetry is generically broken, but it is preserved for special values of the masses where a new branch opens up and the model becomes super-conformal.
Extended Pi-Sigma tilde orbital model for CO adsorption on Pt and Ru
Mion, Thomas; Dimakis, Nicholas; Alamgir, Faisal; Jaye, Cherno; Fischer, Daniel; McGinn, Paul; Cooper, James; Greenbaum, Steve; Smotkin, Eugene
2011-03-01
Several discrepencies between the predicted Blyholder-type adsobtion models and experimental, as well as DFT calculated infared spectra have been addressed for atop CO on Pt in contrast to Ru. This model correlates increased Near Edge X-Ray Absorbtion Fine Structure intensity as the result of a sub-eV downshift from CO on Ru compared to CO on Pt thereby forming a weaker C-O bond. The model accounts for the hybrid orbitals electron transfer between the CO - metal bonds while taking in to consideration the orbital polarization within the CO itself. The charge redistribution of the s-tilde orbitals and reduced charge donation from CO to the surface results in a weaker internal CO bond upon Ru relative to Pt. The extended Pi-Sigma model explains why atop C-O stretching frequencies do not correlate with carbon p-type vacancies. Calculations done on the High Performance Computing Cluster at UT-Pan American. NEXAFS was done on U7A NIST/DOW beamline at Brookheaven National Synchrotron Light Source with funding from the Army Research Office.
Differential Renormalization, the Action Principle and Renormalization Group Calculations
Smirnov, V. A.
1994-01-01
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action principle in the framework of differential renormalization is discussed.
Renormalization: an advanced overview
Gurau, Razvan; Sfondrini, Alessandro
2014-01-01
We present several approaches to renormalization in QFT: the multi-scale analysis in perturbative renormalization, the functional methods \\`a la Wetterich equation, and the loop-vertex expansion in non-perturbative renormalization. While each of these is quite well-established, they go beyond standard QFT textbook material, and may be little-known to specialists of each other approach. This review is aimed at bridging this gap.
Merker, L.; Weichselbaum, A.; Costi, T. A.
2012-08-01
Recent developments in the numerical renormalization group (NRG) allow the construction of the full density matrix (FDM) of quantum impurity models [see A. Weichselbaum and J. von Delft, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.99.076402 99, 076402 (2007)] by using the completeness of the eliminated states introduced by F. B. Anders and A. Schiller [F. B. Anders and A. Schiller, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.95.196801 95, 196801 (2005)]. While these developments prove particularly useful in the calculation of transient response and finite-temperature Green's functions of quantum impurity models, they may also be used to calculate thermodynamic properties. In this paper, we assess the FDM approach to thermodynamic properties by applying it to the Anderson impurity model. We compare the results for the susceptibility and specific heat to both the conventional approach within NRG and to exact Bethe ansatz results. We also point out a subtlety in the calculation of the susceptibility (in a uniform field) within the FDM approach. Finally, we show numerically that for the Anderson model, the susceptibilities in response to a local and a uniform magnetic field coincide in the wide-band limit, in accordance with the Clogston-Anderson compensation theorem.
Energy Technology Data Exchange (ETDEWEB)
Antonov, N V; Kapustin, A S, E-mail: nikolai.antonov@pobox.spbu.r [Department of Theoretical Physics, St Petersburg State University, Uljanovskaja 1, St Petersburg, Petrodvorez 198504 (Russian Federation)
2010-10-08
Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a non-conserved order parameter. The second one is the strongly non-equilibrium reaction-diffusion system known as Gribov process and equivalent to the Reggeon field theory. The turbulent mixing is modelled by the Kazantsev-Kraichnan 'rapid-change' ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum {approx}k{sup -d-{xi}}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent {xi} and the spatial dimension d, both the systems exhibit four different types of critical behaviour, associated with four possible fixed points of the renormalization group equations. Three fixed points correspond to known regimes: Gaussian fixed point, original model without mixing and passively advected scalar field. The most interesting fourth point corresponds to a new type of critical behaviour, in which both nonlinearity and turbulent mixing are relevant, and the critical exponents depend on d, {xi} and the degree of compressibility. The critical exponents and regions of stability for all the regimes are calculated in the leading order of the double expansion in two parameters {xi} and {epsilon} = 4 - d. For both models, compressibility enhances the role of the nonlinear terms in the dynamical equations: the region in the {epsilon}-{xi} plane, where the new nontrivial regime is stable, is getting much wider as the degree of compressibility increases. For the incompressible fluid, the most realistic values d = 3 and {xi} = 4/3 (Kolmogorov turbulence) lie in the region of stability of the passive scalar regime. If the compressibility becomes strong enough, the crossover in the critical behaviour occurs, and these values of d and {xi} fall into the region
Renormalization Scheme Dependence and the Renormalization Group Beta Function
Chishtie, F. A.; McKeon, D. G. C.
2016-01-01
The renormalization that relates a coupling "a" associated with a distinct renormalization group beta function in a given theory is considered. Dimensional regularization and mass independent renormalization schemes are used in this discussion. It is shown how the renormalization $a^*=a+x_2a^2$ is related to a change in the mass scale $\\mu$ that is induced by renormalization. It is argued that the infrared fixed point is to be a determined in a renormalization scheme in which the series expan...
Resurgence and Dynamics of O(N) and Grassmannian Sigma Models
Dunne, Gerald V
2015-01-01
We study the non-perturbative dynamics of the two dimensional ${O(N)}$ and Grassmannian sigma models by using compactification with twisted boundary conditions on $\\mathbb R \\times S^1$, semi-classical techniques and resurgence. While the $O(N)$ model has no instantons for $N>3$, it has (non-instanton) saddles on $\\mathbb R^2$, which we call 2d-saddles. On $\\mathbb R \\times S^1$, the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the ${\\frak o}(N) $ algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in $O(N)$ models in compactified space are in one-to-one correspondence with monopole-instanton saddles in $SO(N)$ gauge theory on $\\mathbb R^3 \\times S^1$. The Grassmannian sig...
The spectrum of Bogomol'nyi solitons in gauged linear $\\sigma$ models
Schroers, B J
1996-01-01
Gauged linear sigma models with C^m-valued scalar fields and gauge group U(1)^d, d \\leq m, have soliton solutions of Bogomol'nyi type if a suitably chosen potential for the scalar fields is also included in the Lagrangian. Here such models are studied on (2+1)-dimensional Minkowski space. If the dynamics of the gauge fields is governed by a Maxwell term the appropriate potential is a sum of generalised Higgs potentials known as Fayet-Iliopoulos D-terms. Many interesting topological solitons of Bogomol'nyi type arise in models of this kind, including various types of vortices (e.g. Nielsen-Olesen semilocal and superconducting vortices) as well as, in certain limits, textures (e.g. CP^(m-1) textures and gauged CP^(m-1) textures). This is explained and general results about the spectrum of topological defects both for broken and partially broken gauge symmetry are proven. When the dynamics of the gauge fields is governed by a Chern-Simons term instead of a Maxwell term a different scalar potential is required fo...
Inheritance principle and Non-renormalization theorems at finite temperature
Brigante, M; Liu, H; Brigante, Mauro; Festuccia, Guido; Liu, Hong
2006-01-01
We show that in the large $N$ limit, a weakly coupled SU(N) gauge theory with adjoint matter on a class of compact manifolds (like $S^3$) satisfies an ``inheritance principle'' in the low temperature phase. Finite temperature correlation functions of gauge invariant single-trace operators are related to those at zero temperature by summing over images of each operator in the Euclidean time direction. This implies that the corresponding finite temperature string theory dual can be formulated as a sigma model with Euclidean time direction periodically compactified. As a consequence, various non-renormalization theorems of $\\NN=4$ Super-Yang-Mills theory survive at finite temperature despite the fact that the conformal and supersymmetries are both broken.
Renormalization of two-dimensional quantum electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Casana S, Rodolfo; Dias, Sebastiao A
1997-12-01
The Schwinger model, when quantized in a gauge non-invariant way exhibits a dependence on a parameter {alpha} (the Jackiw-Rajaraman parameter) in a way which is analogous to the case involving chiral fermions (the chiral Schwinger model). For all values of a {alpha}1, there are divergences in the fermionic Green`s functions. We propose a regularization of the generating functional Z [{eta}, {eta}, J] and we use it to renormalize the theory to one loop level, in a semi-perturbative sense. At the end of the renormalization procedure we find an implicit dependence of {alpha} on the renormalization scale {mu}. (author) 26 refs.
The two-phase issue in the O(n) non-linear $\\sigma$-model: A Monte Carlo study
Alles, B.; Buonanno, A.; Cella, G.
1996-01-01
We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.
Carter, Pam
2010-12-01
When I was first introduced to the Six Sigma process, I resisted it with every ounce of energy I had. I continuously fabricated reasons so that I was unable to complete the training that my company required. When it came time for my performance review, I could not hide the truth from my manager; I had not completed the required training. It was then that I began my journey into the world of Six Sigma. Once I understood that a black belt and a green belt certification had nothing to do with karate, I felt much better.
Development of a Mathematical Model for Multivariate Process by Balanced Six Sigma
Díaz-Castellanos Elizabeth Eugenia; Díaz- Ramos Carlos; Barroso-Moreno Luis Alberto; Pico-González Beatriz
2015-01-01
The Six Sigma methodology is widely used in business to improve quality, increase productivity and lower costs, impacting on business improvement. However, today the challenge is to use those tools for improvements that will have a direct impact on the differentiation of value, which requires the alignment of Six Sigma with the competitive strategies of the organization.Hence the importance of a strategic management system to measure, analyze, improve and control corporate p...
T-duality without isometry via extended gauge symmetries of 2D sigma models
Energy Technology Data Exchange (ETDEWEB)
Chatzistavrakidis, Athanasios [Institut für Theoretische Physik, Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Nijenborgh 4, 9747 AG Groningen (Netherlands); Deser, Andreas [Institut für Theoretische Physik, Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Jonke, Larisa [Division of Theoretical Physics, Rudjer Boković Institute,Bijenika 54, 10000 Zagreb (Croatia)
2016-01-26
Target space duality is one of the most profound properties of string theory. However it customarily requires that the background fields satisfy certain invariance conditions in order to perform it consistently; for instance the vector fields along the directions that T-duality is performed have to generate isometries. In the present paper we examine in detail the possibility to perform T-duality along non-isometric directions. In particular, based on a recent work of Kotov and Strobl, we study gauged 2D sigma models where gauge invariance for an extended set of gauge transformations imposes weaker constraints than in the standard case, notably the corresponding vector fields are not Killing. This formulation enables us to follow a procedure analogous to the derivation of the Buscher rules and obtain two dual models, by integrating out once the Lagrange multipliers and once the gauge fields. We show that this construction indeed works in non-trivial cases by examining an explicit class of examples based on step 2 nilmanifolds.
Energy Technology Data Exchange (ETDEWEB)
Brodsky, Stanley J.; /SLAC; Wu, Xing-Gang; /Chongqing U.
2012-04-02
The uncertainty in setting the renormalization scale in finite-order perturbative QCD predictions using standard methods substantially reduces the precision of tests of the Standard Model in collider experiments. It is conventional to choose a typical momentum transfer of the process as the renormalization scale and take an arbitrary range to estimate the uncertainty in the QCD prediction. However, predictions using this procedure depend on the choice of renormalization scheme, leave a non-convergent renormalon perturbative series, and moreover, one obtains incorrect results when applied to QED processes. In contrast, if one fixes the renormalization scale using the Principle of Maximum Conformality (PMC), all non-conformal {l_brace}{beta}{sub i}{r_brace}-terms in the perturbative expansion series are summed into the running coupling, and one obtains a unique, scale-fixed, scheme-independent prediction at any finite order. The PMC renormalization scale {mu}{sub R}{sup PMC} and the resulting finite-order PMC prediction are both to high accuracy independent of choice of the initial renormalization scale {mu}{sub R}{sup init}, consistent with renormalization group invariance. Moreover, after PMC scale-setting, the n!-growth of the pQCD expansion is eliminated. Even the residual scale-dependence at fixed order due to unknown higher-order {l_brace}{beta}{sub i}{r_brace}-terms is substantially suppressed. As an application, we apply the PMC procedure to obtain NNLO predictions for the t{bar t}-pair hadroproduction cross-section at the Tevatron and LHC colliders. There are no renormalization scale or scheme uncertainties, thus greatly improving the precision of the QCD prediction. The PMC prediction for {sigma}{sub t{bar t}} is larger in magnitude in comparison with the conventional scale-setting method, and it agrees well with the present Tevatron and LHC data. We also verify that the initial scale-independence of the PMC prediction is satisfied to high accuracy at the
Koehl, Patrice; Poitevin, Frédéric; Navaza, Rafael; Delarue, Marc
2017-03-14
Understanding the dynamics of biomolecules is the key to understanding their biological activities. Computational methods ranging from all-atom molecular dynamics simulations to coarse-grained normal-mode analyses based on simplified elastic networks provide a general framework to studying these dynamics. Despite recent successes in studying very large systems with up to a 100,000,000 atoms, those methods are currently limited to studying small- to medium-sized molecular systems due to computational limitations. One solution to circumvent these limitations is to reduce the size of the system under study. In this paper, we argue that coarse-graining, the standard approach to such size reduction, must define a hierarchy of models of decreasing sizes that are consistent with each other, i.e., that each model contains the information of the dynamics of its predecessor. We propose a new method, Decimate, for generating such a hierarchy within the context of elastic networks for normal-mode analysis. This method is based on the concept of the renormalization group developed in statistical physics. We highlight the details of its implementation, with a special focus on its scalability to large systems of up to millions of atoms. We illustrate its application on two large systems, the capsid of a virus and the ribosome translation complex. We show that highly decimated representations of those systems, containing down to 1% of their original number of atoms, still capture qualitatively and quantitatively their dynamics. Decimate is available as an OpenSource resource.
Renormalization group approach to the Fröhlich polaron model: application to impurity-BEC problem
Grusdt, F.; Shchadilova, Y. E.; Rubtsov, A. N.; Demler, E.
2015-01-01
When a mobile impurity interacts with a many-body system, such as a phonon bath, a polaron is formed. Despite the importance of the polaron problem for a wide range of physical systems, a unified theoretical description valid for arbitrary coupling strengths is still lacking. Here we develop a renormalization group approach for analyzing a paradigmatic model of polarons, the so-called Fröhlich model, and apply it to a problem of impurity atoms immersed in a Bose-Einstein condensate of ultra cold atoms. Polaron energies obtained by our method are in excellent agreement with recent diagrammatic Monte Carlo calculations for a wide range of interaction strengths. They are found to be logarithmically divergent with the ultra-violet cut-off, but physically meaningful regularized polaron energies are also presented. Moreover, we calculate the effective mass of polarons and find a smooth crossover from weak to strong coupling regimes. Possible experimental tests of our results in current experiments with ultra cold atoms are discussed. PMID:26183614
Exact Renormalization of Massless QED2
Casana, R; Casana, Rodolfo; Dias, Sebastiao Alves
2001-01-01
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Exact Renormalization of Massless QED2
Casana, Rodolfo; Dias, Sebastião Alves
We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.
Antenucci, F; Crisanti, A; Leuzzi, L
2014-07-01
The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.
Instantons in 2D U(1) Higgs model and 2D CP(N-1) sigma models
Lian, Yaogang
2007-12-01
In this thesis I present the results of a study of the topological structures of 2D U(1) Higgs model and 2D CP N-1 sigma models. Both models have been studied using the overlap Dirac operator construction of topological charge density. The overlap operator provides a more incisive probe into the local topological structure of gauge field configurations than the traditional plaquette-based operator. In the 2D U(1) Higgs model, we show that classical instantons with finite sizes violate the negativity of topological charge correlator by giving a positive contribution to the correlator at non-zero separation. We argue that instantons in 2D U(1) Higgs model must be accompanied by large quantum fluctuations in order to solve this contradiction. In 2D CPN-1 sigma models, we observe the anomalous scaling behavior of the topological susceptibility chi t for N ≤ 3. The divergence of chi t in these models is traced to the presence of small instantons with a radius of order a (= lattice spacing), which are directly observed on the lattice. The observation of these small instantons provides detailed confirmation of Luscher's argument that such short-distance excitations, with quantized topological charge, should be the dominant topological fluctuations in CP1 and CP 2, leading to a divergent topological susceptibility in the continuum limit. For the CPN-1 models with N > 3 the topological susceptibility is observed to scale properly with the mass gap. Another topic presented in this thesis is an implementation of the Zolotarev optimal rational approximation for the overlap Dirac operator. This new implementation has reduced the time complexity of the overlap routine from O(N3 ) to O(N), where N is the total number of sites on the lattice. This opens up a door to more accurate lattice measurements in the future.
A world-line framework for 1D Topological Conformal sigma-models
Baulieu, L; Toppan, F
2015-01-01
We use world-line methods for pseudo-supersymmetry to construct $sl(2|1)$-invariant actions for the $(2,2,0)$ chiral and ($1,2,1)$ real supermultiplets of the twisted $D$-module representations of the $sl(2|1)$ superalgebra. The derived one-dimensional topological conformal $\\sigma$-models are invariant under nilpotent operators. The actions are constructed for both parabolic and hyperbolic/trigonometric realizations (with extra potential terms in the latter case). The scaling dimension $\\lambda$ of the supermultiplets defines a coupling constant, $2\\lambda+1$, the free theories being recovered at $\\lambda=-\\frac{1}{2}$. We also present, generalizing previous works, the $D$-module representations of one-dimensional superconformal algebras induced by ${\\cal N}=(p,q)$ pseudo-supersymmetry acting on $(k,n,n-k)$ supermultiplets. Besides $sl(2|1)$, we obtain the superalgebras $A(1,1)$, $D(2,1;\\alpha)$, $D(3,1)$, $D(4,1)$, $A(2,1)$ from $(p,q)= (1,1), (2,2), (3,3), (4,4), (5,1)$, at given $k,n$ and critical values ...
Modelling of Sigma Scorpii, a high-mass binary with a Beta Cep variable primary component
Tkachenko, A; Pavlovski, K; Degroote, P; Papics, P I; Moravveji, E; Lehmann, H; Kolbas, V; Clemer, K
2014-01-01
High-mass binary stars are known to show an unexplained discrepancy between the dynamical masses of the individual components and those predicted by models. In this work, we study Sigma Scorpii, a double-lined spectroscopic binary system consisting of two B-type stars residing in an eccentric orbit. The more massive primary component is a Beta Cep-type pulsating variable star. Our analysis is based on a time-series of some 1000 high-resolution spectra collected with the CORALIE spectrograph in 2006, 2007, and 2008. We use two different approaches to determine the orbital parameters of the star; the spectral disentangling technique is used to separate the spectral contributions of the individual components in the composite spectra. The non-LTE based spectrum analysis of the disentangled spectra reveals two stars of similar spectral type and atmospheric chemical composition. Combined with the orbital inclination angle estimate found in the literature, our orbital elements allow a mass estimate of 14.7 +/- 4.5 a...
Localization of twisted N=(0,2) gauged linear sigma models in two dimensions
Energy Technology Data Exchange (ETDEWEB)
Closset, Cyril [Simons Center for Geometry and Physics, State University of New York, Stony Brook, NY 11794 (United States); Gu, Wei [Department of Physics MC 0435, Virginia Tech, 850 West Campus Drive, Blacksburg, VA 24061 (United States); Jia, Bei [Theory Group, Physics Department, University of Texas, Austin, TX 78612 (United States); Sharpe, Eric [Department of Physics MC 0435, Virginia Tech, 850 West Campus Drive, Blacksburg, VA 24061 (United States)
2016-03-14
We study two-dimensional N=(0,2) supersymmetric gauged linear sigma models (GLSMs) using supersymmetric localization. We consider N=(0,2) theories with an R-symmetry, which can always be defined on curved space by a pseudo-topological twist while preserving one of the two supercharges of flat space. For GLSMs which are deformations of N=(2,2) GLSMs and retain a Coulomb branch, we consider the A/2-twist and compute the genus-zero correlation functions of certain pseudo-chiral operators, which generalize the simplest twisted chiral ring operators away from the N=(2,2) locus. These correlation functions can be written in terms of a certain residue operation on the Coulomb branch, generalizing the Jeffrey-Kirwan residue prescription relevant for the N=(2,2) locus. For abelian GLSMs, we reproduce existing results with new formulas that render the quantum sheaf cohomology relations and other properties manifest. For non-abelian GLSMs, our methods lead to new results. As an example, we briefly discuss the quantum sheaf cohomology of the Grassmannian manifold.
eta/s and the phase transition of the Non-Linear Sigma Model
Dobado, Antonio; Torres-Rincon, Juan M
2008-01-01
We present a calculation of eta/s for the meson gas (zero baryon number) within unitarized NLO chiral perturbation theory and confirm the observation that eta/s decreases towards the possible phase transition to a quark-gluon plasma/liquid. The value is however somewhat higher than previously estimated in LO chiPT. We then study the behavior of the viscosity over entropy density across the known second order phase transition in the Non-Linear Sigma Model, and establish that it has indeed a minimum that, within calculational uncertainties, can be identified with the phase transition. Finally we examine the case of atomic Argon gas to check the discontinuity of eta/s across a first order phase transition. Our results reinforce the possibility of employing the KSS number to pin down the phase transition and critical point to a cross-over in strongly interacting nuclear matter between the hadron gas and the quark and gluon plasma/liquid.
The Massive O(N) Non-linear Sigma Model at High Orders
Bijnens, Johan
2010-01-01
We extend our earlier work on the massive $O(N)$ nonlinear sigma model to other observables. We derive expressions at leading order in the large $N$ expansion at all orders in the loop expansion for the decay constant, vacuum expectation value, meson-meson scattering and the scalar and vector form factors. This is done using cactus diagram resummation using a generalized gap equation and other recursion relations. For general $N$ we derive the expressions for the $n$-th loop order leading logarithms $\\left(M^2/F^2\\log(\\mu^2/M^2)\\right)^n$, up to five-loops for the decay constant and vacuum expectation value (VEV) and up to four-loops for meson-meson scattering, the scalar and vector form factors. We also quote our earlier result for the mass. The large $N$ results do not give a good approximation for the case $N=3$. We use our results to study the convergence of the perturbative series and compare with elastic unitarity.
Practical Algebraic Renormalization
Grassi, P A; Steinhauser, M
1999-01-01
A practical approach is presented which allows the use of a non-invariant regularization scheme for the computation of quantum corrections in perturbative quantum field theory. The theoretical control of algebraic renormalization over non-invariant counterterms is translated into a practical computational method. We provide a detailed introduction into the handling of the Slavnov-Taylor and Ward-Takahashi identities in the Standard Model both in the conventional and the background gauge. Explicit examples for their practical derivation are presented. After a brief introduction into the Quantum Action Principle the conventional algebraic method which allows for the restoration of the functional identities is discussed. The main point of our approach is the optimization of this procedure which results in an enormous reduction of the calculational effort. The counterterms which have to be computed are universal in the sense that they are independent of the regularization scheme. The method is explicitly illustra...
Gutzwiller renormalization group
Lanatà, Nicola; Yao, Yong-Xin; Deng, Xiaoyu; Wang, Cai-Zhuang; Ho, Kai-Ming; Kotliar, Gabriel
2016-01-01
We develop a variational scheme called the "Gutzwiller renormalization group" (GRG), which enables us to calculate the ground state of Anderson impurity models (AIM) with arbitrary numerical precision. Our method exploits the low-entanglement property of the ground state of local Hamiltonians in combination with the framework of the Gutzwiller wave function and indicates that the ground state of the AIM has a very simple structure, which can be represented very accurately in terms of a surprisingly small number of variational parameters. We perform benchmark calculations of the single-band AIM that validate our theory and suggest that the GRG might enable us to study complex systems beyond the reach of the other methods presently available and pave the way to interesting generalizations, e.g., to nonequilibrium transport in nanostructures.
Tensor Network Renormalization.
Evenbly, G; Vidal, G
2015-10-30
We introduce a coarse-graining transformation for tensor networks that can be applied to study both the partition function of a classical statistical system and the Euclidean path integral of a quantum many-body system. The scheme is based upon the insertion of optimized unitary and isometric tensors (disentanglers and isometries) into the tensor network and has, as its key feature, the ability to remove short-range entanglement or correlations at each coarse-graining step. Removal of short-range entanglement results in scale invariance being explicitly recovered at criticality. In this way we obtain a proper renormalization group flow (in the space of tensors), one that in particular (i) is computationally sustainable, even for critical systems, and (ii) has the correct structure of fixed points, both at criticality and away from it. We demonstrate the proposed approach in the context of the 2D classical Ising model.
Two species of vortices in massive gauged non-linear sigma models
Energy Technology Data Exchange (ETDEWEB)
Alonso-Izquierdo, A. [Departamento de Matemática Aplicada, Universidad de Salamanca,Facultad de Ciencias Agrarias y Ambientales, Av. Filiberto Villalobos 119, E-37008 Salamanca (Spain); Fuertes, W. García [Departamento de Física, Universidad de Oviedo, Facultad de Ciencias, Calle Calvo Sotelo s/n, E-33007 Oviedo (Spain); Guilarte, J. Mateos [Departamento de Física Fundamental, Universidad de Salamanca, Facultad de Ciencias, Plaza de la Merced, E-37008 Salamanca (Spain)
2015-02-23
Non-linear sigma models with scalar fields taking values on ℂℙ{sup n} complex manifolds are addressed. In the simplest n=1 case, where the target manifold is the S{sup 2} sphere, we describe the scalar fields by means of stereographic maps. In this case when the U(1) symmetry is gauged and Maxwell and mass terms are allowed, the model accommodates stable self-dual vortices of two kinds with different energies per unit length and where the Higgs field winds at the cores around the two opposite poles of the sphere. Allowing for dielectric functions in the magnetic field, similar and richer self-dual vortices of different species in the south and north charts can be found by slightly modifying the potential. Two different situations are envisaged: either the vacuum orbit lies on a parallel in the sphere, or one pole and the same parallel form the vacuum orbit. Besides the self-dual vortices of two species, there exist BPS domain walls in the second case. Replacing the Maxwell contribution of the gauge field to the action by the second Chern-Simons secondary class, only possible in (2+1)-dimensional Minkowski space-time, new BPS topological defects of two species appear. Namely, both BPS vortices and domain ribbons in the south and the north charts exist because the vacuum orbit consits of the two poles and one parallel. Formulation of the gauged ℂℙ{sup 2} model in a reference chart shows a self-dual structure such that BPS semi-local vortices exist. The transition functions to the second or third charts break the U(1)×SU(2) semi-local symmetry, but there is still room for standard self-dual vortices of the second species. The same structures encompassing N complex scalar fields are easily generalized to gauged ℂℙ{sup N} models.
Renormalization and effective lagrangians
Polchinski, Joseph
1984-01-01
There is a strong intuitive understanding of renormalization, due to Wilson, in terms of the scaling of effective lagrangians. We show that this can be made the basis for a proof of perturbative renormalization. We first study renormalizability in the language of renormalization group flows for a toy renormalization group equation. We then derive an exact renormalization group equation for a four-dimensional λø 4 theory with a momentum cutoff. We organize the cutoff dependence of the effective lagrangian into relevant and irrelevant parts, and derive a linear equation for the irrelevant part. A lengthy but straightforward argument establishes that the piece identified as irrelevant actually is so in perturbation theory. This implies renormalizability. The method extends immediately to any system in which a momentum-space cutoff can be used, but the principle is more general and should apply for any physical cutoff. Neither Weinberg's theorem nor arguments based on the topology of graphs are needed.