Exact renormalization group and Sine Gordon theory
Oak, Prafulla; Sathiapalan, B.
2017-07-01
The exact renormalization group is used to study the RG flow of quantities in field theories. The basic idea is to write an evolution operator for the flow and evaluate it in perturbation theory. This is easier than directly solving the differential equation. This is illustrated by reproducing known results in four dimensional ϕ 4 field theory and the two dimensional Sine-Gordon theory. It is shown that the calculation of beta function is somewhat simplified. The technique is also used to calculate the c-function in two dimensional Sine-Gordon theory. This agrees with other prescriptions for calculating c-functions in the literature. If one extrapolates the connection between central charge of a CFT and entanglement entropy in two dimensions, to the c-function of the perturbed CFT, then one gets a value for the entanglement entropy in Sine-Gordon theory that is in exact agreement with earlier calculations (including one using holography) in arXiv:1610.04233.
Spectrum of boundary states in N=1 SUSY sine-Gordon theory
Bajnok, Z; Takács, G
2002-01-01
We consider N=1 supersymmetric sine-Gordon theory (SSG) with supersymmetric integrable boundary conditions (boundary SSG = BSSG). We find two possible ways to close the boundary bootstrap for this model, corresponding to two different choices for the boundary supercharge. We argue that these two bootstrap solutions should correspond to the two integrable Lagrangian boundary theories considered recently by Nepomechie.
Sine-Gordon Theory : Entanglement entropy and holography
Banerjee, Pinaki; Sathiapalan, B
2016-01-01
We compute entanglement entropy of sine-Gordon theory for a single interval using both field theoretic and holographic techniques. The results match for near-marginal perturbations up to leading order in the coupling.
Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
Matsui, Chihiro
2014-01-01
We discussed subspaces of the N=1 supersymmetric sine-Gordon model with Dirichlet boundaries through light-cone lattice regularization. In this paper, we showed, unlike the periodic boundary case, both of Neveu-Schwarz (NS) and Ramond (R) sectors of a superconformal field theory were obtained. Using a method of nonlinear integral equations for auxiliary functions defined by eigenvalues of transfer matrices, we found that an excitation state with an odd number of particles is allowed for a certain value of a boundary parameter even on a system consisting of an even number of sites. In a small-volume limit where conformal invariance shows up in the theory, we derived conformal dimensions of states constructed through the lattice-regularized theory. The result shows existence of the R sector, which cannot be obtained from the periodic system, while a winding number is restricted to an integer or a half-integer depending on boundary parameters.
Vortex Strings and Nonabelian sine-Gordon Theories
Park, Q H
1999-01-01
We generalize the Lund-Regge model for vortex string dynamics in 4-dimensional Minkowski space to the arbitrary n-dimensional case. The n-dimensional vortex equation is identified with a nonabelian sine-Gordon equation and its integrability is proven by finding the associated linear equations of the inverse scattering. An explicit expression of vortex coordinates in terms of the variables of the nonabelian sine-Gordon system is derived. In particular, we obtain the n-dimensional vortex soliton solution of the Hasimoto-type from the one soliton solution of the nonabelian sine-Gordon equation.
Nonabelian sine-Gordon theory and its application to nonlinear optics
Park, Q H; Park, Q Han
1996-01-01
Using a field theory generalization of the spinning top motion, we construct nonabelian generalizations of the sine-Gordon theory according to each symmetric spaces. A Lagrangian formulation of these generalized sine-Gordon theories is given in terms of a deformed gauged Wess-Zumino-Witten action which also accounts for integrably perturbed coset conformal field theories. As for physical applications, we show that they become precisely the effective field theories of self-induced transparency in nonlinear optics. This provides a dictionary between field theory and nonlinear optics.
SUSY sine-Gordon theory as a perturbed conformal field theory and finite size effects
Bajnok, Z; Palla, L; Takács, G; Wagner, F
2004-01-01
We consider SUSY sine-Gordon theory in the framework of perturbed conformal field theory. Using an argument from Zamolodchikov, we obtain the vacuum structure and the kink adjacency diagram of the theory, which is cross-checked against the exact S matrix prediction, first-order perturbed conformal field theory (PCFT), the NLIE method and truncated conformal space approach. We provide evidence for consistency between the usual Lagrangian description and PCFT on the one hand, and between PCFT, NLIE and a massgap formula conjectured by Baseilhac and Fateev, on the other. In addition, we extend the NLIE description to all the vacua of the theory.
Koller, Andrew; Olshanii, Maxim
2011-12-01
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schrödinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t) = (nh/τ)/cosh(t/τ), with n being an integer and τ being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.
Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
Blas, H
2007-01-01
The solitons and kinks of the generalized $sl(3, \\IC)$ sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the {\\sl tau} functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the $sl(3, \\IC)$ affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized $sl(3, \\IC)$ sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for "quark" confinement.
Solitons, kinks and extended hadron model based on the generalized sine-Gordon theory
Energy Technology Data Exchange (ETDEWEB)
Blas, Harold [Departamentos de Matematica e Fisica - ICET, Universidade Federal de Mato Grosso, Av. Fernando Correa, s/n, Coxipo, 78060-900, Cuiaba - MT (Brazil); Carrion, Hector L. [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, 05315-970, Sao Paulo, SP (Brazil)
2007-01-15
The solitons and kinks of the generalized sl(3,C) sine-Gordon (GSG) model are explicitly obtained through the hybrid of the Hirota and dressing methods in which the tau functions play an important role. The various properties are investigated, such as the potential vacuum structure, the soliton and kink solutions, and the soliton masses formulae. As a reduced submodel we obtain the double sine-Gordon model. Moreover, we provide the algebraic construction of the sl(3,C) affine Toda model coupled to matter (Dirac spinor) (ATM) and through a gauge fixing procedure we obtain the classical version of the generalized sl(3,C) sine-Gordon model (cGSG) which completely decouples from the Dirac spinors. In the spinor sector we are left with Dirac fields coupled to cGSG fields. Based on the equivalence between the U(1) vector and topological currents it is shown the confinement of the spinors inside the solitons and kinks of the cGSG model providing an extended hadron model for 'quark' confinement.
The (1+1)-dimensional Massive sine-Gordon Field Theory and the Gaussian Wave-functional Approach
Lu, W F
1999-01-01
The ground, one- and two-particle states of the (1+1)-dimensional massive sine-Gordon field theory are investigated within the framework of the Gaussian wave-functional approach. We demonstrate that for a certain region of the model-parameter space, the vacuum in the field system is asymmetrical, which verifies an earlier conjecture. Furthermore, it is shown that two-particle bound state can exist upon the asymmetric vacuum for some portion of the aforementioned region. Besides, the masses of one particle and tow-particle bound state upon the symmetric vacuum are also calculated, and the resultant masses agree with the recent second-order results of fermion-mass perturbation for the massive Schwinger model.
From B(a)cklund Transformation to a Linear System of Sine-Gordon Theory in Superspace
Institute of Scientific and Technical Information of China (English)
M. Siddiq; M. Hassan
2005-01-01
@@ A systematic approach is presented to find a linear system associated with the sine-Gordon equation from a given set of super Riccati systems. The Riccati system is shown to be related to the super B(a)cklund transformation and the linear eigenvalue problem.
Generalized sine-Gordon solitons
Energy Technology Data Exchange (ETDEWEB)
Santos, C dos [Centro de Fisica e Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, 4169-007 Porto (Portugal); Rubiera-Garcia, D, E-mail: cssilva@fc.up.pt, E-mail: rubieradiego@gmail.com [Departamento de Fisica, Universidad de Oviedo, Avenida Calvo Sotelo 18, 33007 Oviedo, Asturias (Spain)
2011-10-21
In this paper, we construct analytical self-dual soliton solutions in (1+1) dimensions for two families of models which can be seen as generalizations of the sine-Gordon system but where the kinetic term is non-canonical. For that purpose we use a projection method applied to the sine-Gordon soliton. We focus our attention on the wall and lump-like soliton solutions of these k-field models. These solutions and their potentials reduce to those of the Klein-Gordon kink and the standard lump for the case of a canonical kinetic term. As we increase the nonlinearity on the kinetic term the corresponding potentials get modified and the nature of the soliton may change, in particular, undergoing a topology modification. The procedure constructed here is shown to be a sort of generalization of the deformation method for a specific class of k-field models. (paper)
Bajnok, Z; Takács, G
2002-01-01
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and checked these results against WKB quantization and numerical finite volume spectra obtained from the truncated conformal space approach. The relation between a boundary resonance state and the semiclassical instability of a static classical solution is analyzed in detail.
Lagrangian formulation of symmetric space sine-Gordon models
Bakas, Ioannis; Shin, H J; Park, Q Han
1996-01-01
The symmetric space sine-Gordon models arise by conformal reduction of ordinary 2-dim \\sigma-models, and they are integrable exhibiting a black-hole type metric in target space. We provide a Lagrangian formulation of these systems by considering a triplet of Lie groups F \\supset G \\supset H. We show that for every symmetric space F/G, the generalized sine-Gordon models can be derived from the G/H WZW action, plus a potential term that is algebraically specified. Thus, the symmetric space sine-Gordon models describe certain integrable perturbations of coset conformal field theories at the classical level. We also briefly discuss their vacuum structure, Backlund transformations, and soliton solutions.
Complex sine-Gordon Equation in Coherent Optical Pulse Propagation
Park, Q H
1999-01-01
It is shown that the McCall-Hahn theory of self-induced transparency in coherent optical pulse propagation can be identified with the complex sine-Gordon theory in the sharp line limit. We reformulate the theory in terms of the deformed gauged Wess-Zumino-Witten sigma model and address various new aspects of self-induced transparency.
Experimental Investigation of Trapped Sine-Gordon Solitons
DEFF Research Database (Denmark)
Davidson, A.; Dueholm, B.; Kryger, B.
1985-01-01
We have observed for the first time a single sine-Gordon soliton trapped in an annular Josephson junction. This system offers a unique possibility to study undisturbed soliton motion. In the context of perturbation theory, the soliton may be viewed as a relativistic particle moving under a uniform...
Energy Technology Data Exchange (ETDEWEB)
Renn, J.; Steinmann, A.
1986-07-01
The upper bound for the ultraviolet stability of the two-dimensional cosine interaction ..integral../sub ..lambda../:cos ..cap alpha..phi/sub xi/:dxi, ..lambda..is contained inR/sup 2/, in finite volume ..lambda.. is proven for ..cap alpha../sup 2/ element of (4..pi..,8..pi..(, where the theory has been shown to be superrenormalizable (see, e.g., G. Gallavotti, Rev. Mod. Phys. 57, 471 (1985)). Ultraviolet stability in this interval was proven previously (F. Nicolo, J. Renn, and A.Steinmann, ''On the massive sine--Gordon equation in all regions of collapse,'' preprint II Universita di Roma, 1985). Here we give a second proof using renormalization group methods based on a multiscale decomposition of the field by showing that the large fluctuations may be controlled by their small probability. The method essentially follows the one given by Nicolo (F. Nicolo, Commun. Math. Phys. 88, 681 (1983)) for ..cap alpha../sup 2/ element of (4..pi.., (32)/(5) ..pi..(.
The Quantum Sine-Gordon Model in Perturbative AQFT
Bahns, Dorothea; Rejzner, Kasia
2017-08-01
We study the Sine-Gordon model with Minkowski signature in the framework of perturbative algebraic quantum field theory. We calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the expectation value—with respect to the vacuum or a Hadamard state—of the Epstein Glaser S-matrix and the interacting current or the field respectively converge, both given as formal power series.
Breather Dynamics of the Sine-Gordon Equation
Institute of Scientific and Technical Information of China (English)
Stephen Johnson; Anjan Biswas
2013-01-01
This paper studies the adiabatic dynamics of the breather soliton of the sine-Gordon equation.The integrals of motion are found and then used in soliton perturbation theory to derive the differential equation governing the soliton velocity.Time-dependent functions arise and their properties are studied.These functions are found to be bounded and periodic and affect the soliton velocity.The soliton velocity is numerically plotted against time for different combinations of initial velocities and perturbation terms.
The Quantum Sine Gordon model in perturbative AQFT
Bahns, Dorothea
2016-01-01
We study the Sine Gordon model in the framework of perturbative algebraic quantum field theory, without making use of a representation on Fock space. In particular, we calculate the vertex operator algebra braiding property. We prove that in the finite regime of the model, the vacuum expectation value of the Epstein Glaser $S$-matrix and the interacting current, both given as formal power series, converge in a suitable topology on the space of functionals.
Gravity localization in sine-Gordon braneworlds
Cruz, W T; Sousa, L J S; Almeida, C A S
2016-01-01
In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a resonance to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massless and massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.
Gravity localization in sine-Gordon braneworlds
Energy Technology Data Exchange (ETDEWEB)
Cruz, W.T., E-mail: wilamicruz@gmail.com [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Juazeiro do Norte, 63040-540 Juazeiro do Norte, Ceará (Brazil); Maluf, R.V., E-mail: r.v.maluf@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará (UFC), C.P. 6030, 60455-760 Fortaleza, Ceará (Brazil); Sousa, L.J.S., E-mail: luisjose@fisica.ufc.br [Instituto Federal de Educação, Ciência e Tecnologia do Ceará (IFCE), Campus Canindé, 62700-000 Canindé, Ceará (Brazil); Almeida, C.A.S., E-mail: carlos@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará (UFC), C.P. 6030, 60455-760 Fortaleza, Ceará (Brazil)
2016-01-15
In this work we study two types of five-dimensional braneworld models given by sine-Gordon potentials. In both scenarios, the thick brane is generated by a real scalar field coupled to gravity. We focus our investigation on the localization of graviton field and the behaviour of the massive spectrum. In particular, we analyse the localization of massive modes by means of a relative probability method in a Quantum Mechanics context. Initially, considering a scalar field sine-Gordon potential, we find a localized state to the graviton at zero mode. However, when we consider a double sine-Gordon potential, the brane structure is changed allowing the existence of massive resonant states. The new results show how the existence of an internal structure can aid in the emergence of massive resonant modes on the brane.
Dilogarithm Identities for Sine-Gordon and Reduced Sine-Gordon Y-Systems
Directory of Open Access Journals (Sweden)
Tomoki Nakanishi
2010-10-01
Full Text Available We study the family of Y-systems and T-systems associated with the sine-Gordon models and the reduced sine-Gordon models for the parameter of continued fractions with two terms. We formulate these systems by cluster algebras, which turn out to be of finite type, and prove their periodicities and the associated dilogarithm identities which have been conjectured earlier. In particular, this provides new examples of periodicities of seeds.
Overlaps after quantum quenches in the sine-Gordon model
Horváth, D. X.; Takács, G.
2017-08-01
We present a numerical computation of overlaps in mass quenches in sine-Gordon quantum field theory using truncated conformal space approach (TCSA). To improve the cut-off dependence of the method, we use a novel running coupling definition which has a general applicability in free boson TCSA. The numerical results for the first breather overlaps are compared with the analytic continuation of a previously proposed analytical Ansatz for the initial state in a related sinh-Gordon quench, and good agreement is found between the numerical data and the analytical prediction in a large energy range.
Bunched soliton states in weakly coupled sine-Gordon systems
DEFF Research Database (Denmark)
Grønbech-Jensen, N.; Samuelsen, Mogens Rugholm; Lomdahl, P. S.
1990-01-01
The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results.......The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results....
Radial sine-Gordon kinks as sources of fast breathers
DEFF Research Database (Denmark)
Caputo, Jean Guy; Sørensen, Mads Peter
2013-01-01
We consider radial sine-Gordon kinks in two, three, and higher dimensions. A full two-dimensional simulation showing that azimuthal perturbations remain small allows us to reduce the problem to the one-dimensional radial sine-Gordon equation. We solve this equation on an interval [r, r1] and abso...
The Geometrodynamics of Sine-Gordon Solitons
Gegenberg, J
1998-01-01
The relationship between N-soliton solutions to the Euclidean sine-Gordon equation and Lorentzian black holes in Jackiw-Teitelboim dilaton gravity is investigated, with emphasis on the important role played by the dilaton in determining the black hole geometry. We show how an N-soliton solution can be used to construct ``sine-Gordon'' coordinates for a black hole of mass M, and construct the transformation to more standard ``Schwarzchild-like'' coordinates. For N=1 and 2, we find explicit closed form solutions to the dilaton equations of motion in soliton coordinates, and find the relationship between the soliton parameters and the black hole mass. Remarkably, the black hole mass is non-negative for arbitrary soliton parameters. In the one-soliton case the coordinates are shown to cover smoothly a region containing the whole interior of the black hole as well as a finite neighbourhood outside the horizon. A Hamiltonian analysis is performed for slicings that approach the soliton coordinates on the interior, a...
Kondo, Kenichi
2013-11-01
Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Directory of Open Access Journals (Sweden)
Kenichi Kondo
2013-11-01
Full Text Available Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained here are considered to directly correspond to the discrete counterpart. We also propose a noncommutative discrete analogue of the sine-Gordon equation, reveal its relations to other integrable systems including the noncommutative discrete KP equation, and construct multisoliton solutions by a repeated application of Darboux transformations. Moreover, we derive a noncommutative ultradiscrete analogue of the sine-Gordon equation and its 1-soliton and 2-soliton solutions, using the symmetrized max-plus algebra. As a result, we have a complete set of commutative and noncommutative versions of continuous, discrete, and ultradiscrete sine-Gordon equations.
Massless Boundary Sine-Gordon Model Coupled to External Fields
Kogetsu, H
2005-01-01
We investigate a generalization of the massless boundary sine-Gordon model with conformal invariance, which has been used to describe an array of D-branes (or rolling tachyon). We consider a similar action whose couplings are replaced with external fields depending on the boundary coordinate. Even in the presence of the external fields, this model is still solvable, though it does not maintain the whole conformal symmetry. We obtain, to all orders in perturbation theory in terms of the external fields, a simpler expression of the boundary state and the disc partition function. As a by-product, we fix the relation between the bare couplings and the renormalized couplings which has been appeared in papers on tachyon lump and rolling tachyon.
A unified approach in seeking the solitary wave solutions to sine-Gordon type equations
Institute of Scientific and Technical Information of China (English)
Xie Yuan-Xi; Tang Jia-Shi
2005-01-01
By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine-Gordon type equations.As illustrative examples, the exact solitary wave solutions of some physically significant sine-Gordon type equations,including the sine-Gordon equation, double sine-Gordon equation and mKdV-sine-Gordon equation, are investigated by means of this method.
Bunched soliton states in weakly coupled sine-Gordon systems
Energy Technology Data Exchange (ETDEWEB)
Gronbech-Jensen, N.; Samuelsen, M.R. (Physics Laboratory I, The Technical University of Denmark, DK-2800 Lyngby (Denmark)); Lomdahl, P.S. (Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM (USA)); Blackburn, J.A. (Department of Physics and Computing, Wilfrid Laurier University, Waterloo, Ontario (Canada))
1990-09-01
The interaction between solitons of two weakly coupled sine-Gordon systems is considered. In particular, the stability of bunched states is investigated, and perturbation results are compared with numerical results.
Boundary states and finite size effects in sine-Gordon model with Neumann boundary condition
Bajnok, Z; Takács, G
2001-01-01
The sine-Gordon model with Neumann boundary condition is investigated. Using the bootstrap principle the spectrum of boundary bound states is established. Somewhat surprisingly it is found that Coleman-Thun diagrams and bound state creation may coexist. A framework to describe finite size effects in boundary integrable theories is developed and used together with the truncated conformal space approach to confirm the bound states and reflection factors derived by bootstrap.
Noncommutative (generalized) sine-Gordon/massive Thirring correspondence, integrability and solitons
Blas, H
2010-01-01
Some properties of the correspondence between the non-commutative versions of the (generalized) sine-Gordon (NCGSG$_{1,2}$) and the massive Thirring (NCGMT$_{1,2}$) models are studied. Our method relies on the master Lagrangian approach to deal with dual theories. The master Lagrangians turn out to be the NC versions of the so-called affine Toda model coupled to matter fields (NCATM$_{1,2}$), in which the Toda field $g$ belongs to certain subgroups of $ GL(3)$, and the matter fields lie in the higher grading directions of an affine Lie algebra. Depending on the form of $g$ one arrives at two different NC versions of the NCGSG$_{1,2}$/NCGMT$_{1,2}$ correspondence. In the NCGSG$_{1,2}$ sectors, through consistent reduction procedures, we find NC versions of some well-known models, such as the NC sine-Gordon (NCSG$_{1,2}$) (Lechtenfeld et al. and Grisaru-Penati proposals, respectively), NC (bosonized) Bukhvostov-Lipatov (NCbBL$_{1,2}$) and NC double sine-Gordon (NCDSG$_{1,2}$) models. The NCGMT$_{1,2}$ models co...
Sudden interaction quench in the quantum sine-Gordon model
Energy Technology Data Exchange (ETDEWEB)
Sabio, Javier [Instituto de Ciencia de Materiales de Madrid (CSIC), Sor Juana Ines de la Cruz 3, E-28049 Madrid (Spain); Kehrein, Stefan, E-mail: javier.sabio@icmm.csic.e [Arnold-Sommerfeld-Center for Theoretical Physics, Center for NanoSciences and Department fuer Physik, Ludwig-Maximilians-Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)
2010-05-15
We study a sudden interaction quench in the weak-coupling regime of the quantum sine-Gordon model. The real time dynamics of the bosonic mode occupation numbers is calculated using the flow equation method. While we cannot prove results for the asymptotic long-time limit, we can establish the existence of an extended regime in time where the mode occupation numbers relax to twice their equilibrium values. This factor two indicates a non-equilibrium distribution and is a universal feature of weak interaction quenches. The weak-coupling quantum sine-Gordon model therefore turns out to be on the borderline between thermalization and non-thermalization.
Abundant Interaction Solutions of Sine-Gordon Equation
Directory of Open Access Journals (Sweden)
DaZhao Lü
2012-01-01
Full Text Available With the help of computer symbolic computation software (e.g., Maple, abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.
Nonlinear dynamics of a parametrically driven sine-Gordon system
DEFF Research Database (Denmark)
Grønbech-Jensen, Niels; Kivshar, Yuri S.; Samuelsen, Mogens Rugholm
1993-01-01
We consider a sine-Gordon system, driven by an ac parametric force in the presence of loss. It is demonstrated that a breather can be maintained in a steady state at half of the external frequency. In the small-amplitude limit the effect is described by an effective nonlinear Schrodinger equation...
Phonons and solitons in the "thermal" sine-Gordon system
DEFF Research Database (Denmark)
Salerno, Mario; Jørgensen, E.; Samuelsen, Mogens Rugholm
1984-01-01
Standard methods of stochastic processes are used to study the coupling of the sine-Gordon system with a heat reservoir. As a result we find thermal phonons with an average energy of kB T per mode. The translational mode (zero mode) is found to carry an average energy of 1 / 2kBT. This last value...
Soliton annihilation in the perturbed sine-Gordon system
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Samuelsen, Mogens Rugholm; Welner, D.
1984-01-01
Fluxon-antifluxon annihilation in the perturbed sine-Gordon equation with loss and driving terms is investigated. For the infinite line we find a simple analytic expression for the threshold driving term corresponding to annihilation. With the application of the results to a Josephson junction...
Perturbation analysis of a parametrically changed sine-Gordon equation
DEFF Research Database (Denmark)
Sakai, S.; Samuelsen, Mogens Rugholm; Olsen, O. H.
1987-01-01
A long Josephson junction with a spatially varying inductance is a physical manifestation of a modified sine-Gordon equation with parametric perturbation. Soliton propagation in such Josephson junctions is discussed. First, for an adiabatic model where the inductance changes smoothly compared...
Rotationally symmetric numerical solutions to the sine-Gordon equation
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
We examine numerically the properties of solutions to the spherically symmetric sine-Gordon equation given an initial profile which coincides with the one-dimensional breather solution and refer to such solutions as ring waves. Expanding ring waves either exhibit a return effect or expand towards...
Bidifferential Calculus, Matrix SIT and Sine-Gordon Equations
Directory of Open Access Journals (Sweden)
A. Dimakis
2011-01-01
Full Text Available We express a matrix version of the self-induced transparency (SIT equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a general result that generates exact solutions from solutions of a linear system of arbitrary matrix size. A side result is a solution formula for the sine-Gordon equation.
Static Properties of the Multiple-Sine-Gordon Systems
Peyravi, M; Montakhab, Afshin
2010-01-01
In this paper, we examine some basic properties of the multiple-Sine-Gordon (MSG) systems, which constitute a generalization of the celebrated sine-Gordon (SG) system. We start by showing how MSG systems can be viewed as a general class of periodic functions. Next, periodic and step-like solutions of these systems are discussed in some details. In particular, we study the static properties of such systems by considering slope and phase diagrams. We also use concepts like energy density and pressure to characterize and distinguish such solutions. We interpret these solutions as an interacting many body system, in which kinks and antikinks behave as extended particles. Finally, we provide a linear stability analysis of periodic solutions which indicates short wavelength solutions to be stable.
Multiresonance modes in sine-Gordon brane models
Cruz, W T; Almeida, C A S
2015-01-01
In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine-Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes
Multiresonance modes in sine-Gordon brane models
Cruz, W. T.; Maluf, R. V.; Dantas, D. M.; Almeida, C. A. S.
2016-12-01
In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine-Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, which is concluded that the dilaton parameter regulates these corrections.
Study of models of the sine-Gordon type in flat and curved spacetime
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Losano, L. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Menezes, R. [Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil); Rocha, Roldao da [Universidade Federal do ABC, Centro de Matematica, Computacao e Cognicao, Santo Andre, SP (Brazil)
2013-07-15
We study a new family of models of the sine-Gordon type, starting from the sine-Gordon model, including the double sine-Gordon, the triple one, and so on. The models appears as deformations of the starting model, with the deformation controlled by two parameters, one very small, used to control a linear expansion on it, and the other, which specifies the particular model in the family of models. We investigate the presence of topological defects, showing how the solutions can be constructed explicitly from the topological defects of the sine-Gordon model itself. In particular, we delve into the double sine-Gordon model in a braneworld scenario with a single extra dimension of infinite extent, showing that a stable gravity scenario is admissible. Also, we briefly show that the deformation procedure can be used iteratively, leading to a diversity of possibilities to construct families of models of the sine-Gordon type. (orig.)
A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections
Aguirre, A R
2016-01-01
We consider one loop quantum corrections to soliton mass for the $N=1$ supersymmetric extension of the $\\phi^2 \\cos^2(\\ln \\phi^2)$ scalar field theory in (1+1) dimensions. First, we compute the one loop quantum soliton mass correction of the bosonic sector by using a mixture of the scattering phase shift and the Euclidean effective action technique. Afterwards the computation in the supersymmetric case is naturally extended by considering the fermionic phase shifts associated to the Majorana fields. As a result we derive a general formula for the one loop quantum corrections to the soliton mass of the SUSY kink, and obtain for this exotic model the same value as for the SUSY sine-Gordon and $\\phi^4$ models.
Quantum sine-Gordon dynamics on analogue curved spacetime in a weakly imperfect scalar Bose gas
Volkoff, T J
2016-01-01
Using the coherent state functional integral formulation of the partition function, we show that the sine-Gordon model on an analogue curved spacetime arises as the effective quantum field theory for phase fluctuations of a weakly imperfect Bose gas on an incompressible background superfluid flow, when these fluctuations are restricted to a subspace of the single-particle Hilbert space. We consider bipartitions of the single-particle Hilbert space relevant to experiments on ultracold bosonic atomic or molecular gases, including, e.g., restriction to high or low energy sectors of the dynamics, and spatial bipartition corresponding to tunnel-coupled planar Bose gases. By assuming full unitary quantum control in the low energy subspace of a trapped gas, we show that: 1) appropriately tuning the particle number statistics of the lowest energy mode partially decouples the low and high energy sectors, allowing any low-energy single-particle wavefunction to define a background for sine-Gordon dynamics on curved spac...
Functional Integrals and Free Energy in sine-Gordon-Thirring Model with Impurity Coupling
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The free energy at low temperature in ID sine-Gordon-Thirring model with impurity coupling is studied by means of functional integrals method. For massive free sine-Gordon-Thirring model, free energy is obtained from perturbation expansion of functional determinant. Moreover, the free energy of massive model is calculated by use of an auxiliary Bose Geld method.
Lattice approach to finite volume form-factors of the Massive Thirring (Sine-Gordon) model
Hegedűs, Árpád
2017-08-01
In this paper we demonstrate, that the light-cone lattice approach for the Massive-Thirring (sine-Gordon) model, through the quantum inverse scattering method, admits an appropriate framework for computing the finite volume form-factors of local operators of the model. In this work we compute the finite volume diagonal matrix elements of the U(1) conserved current in the pure soliton sector of the theory. Based on the systematic large volume expansion of our results, we conjecture an exact expression for the finite volume expectation values of local operators in pure soliton states. At large volume in leading order these expectation values have the same form as in purely elastic scattering theories, but exponentially small corrections differ from previous Thermodynamic Bethe Ansatz conjectures of purely elastic scattering theories.
Multisymplectic approach to integrable defects in the sine-Gordon model
Caudrelier, Vincent
2014-01-01
Ideas from the theory of multisymplectic systems, introduced recently in integrable systems by the author and Kundu to discuss Liouville integrability in classical field theories with a defect, are applied to the sine-Gordon model. The key ingredient is the introduction of a second Poisson bracket in the theory that allows for a Hamiltonian description of the model that is completely equivalent to the standard one, in the absence of a defect. In the presence of a defect described by frozen B\\"acklund transformations, our approach based on the new bracket unifies the various tools used so far to attack the problem. It also gets rid of the known issues related to the evaluation of the Poisson brackets of the defect matrix which involve fields at coinciding space point (the location of the defect). The original Lagrangian approach also finds a nice reinterpretation in terms of the canonical transformation representing the defect conditions.
Supersymmetric invariant theories
Esipova, S R; Radchenko, O V
2013-01-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Supersymmetric invariant theories
Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.
2014-04-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Kink propagation and trapping in a two dimensional curved sine-Gordon system
DEFF Research Database (Denmark)
Sørensen, Mads Peter
The sine-Gordon equation is one of the three classical nonlinear partial differential equations possessing soliton solutions in the case of one spatial dimension. Extending the sine-Gordon equation to two spatial dimensions is relevant for applications to the dynamics of large area Josephson...... to investigate how kink shaped solitons of the sine-Gordon equation propagate through the bent section. We have found that the region with finite curvature acts as a potential barrier whose height and width depends on the radius of curvature of the waveguide. The kink transmission, reflection and trapping...
Kink propagation and trapping in a two dimensional curved sine-Gordon system
DEFF Research Database (Denmark)
Sørensen, Mads Peter
The sine-Gordon equation is one of the three classical nonlinear partial differential equations possessing soliton solutions in the case of one spatial dimension. Extending the sine-Gordon equation to two spatial dimensions is relevant for applications to the dynamics of large area Josephson...... to investigate how kink shaped solitons of the sine-Gordon equation propagate through the bent section. We have found that the region with finite curvature acts as a potential barrier whose height and width depends on the radius of curvature of the waveguide. The kink transmission, reflection and trapping...
Sine-Gordon solitons in networks: Scattering and transmission at vertices
Sobirov, Zarif; Babajanov, Doniyor; Matrasulov, Davron; Nakamura, Katsuhiro; Uecker, Hannes
2016-09-01
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws together with successive space-derivatives of sine-Gordon equation. We analytically obtain traveling-wave solutions in the form of standard sine-Gordon solitons such as kinks and antikinks for star and tree graphs. We show that for this case the sine-Gordon equation becomes completely integrable just as in case of a simple 1D chain. This simple analysis provides a cornerstone for the numerical solution of the general case, including a quantification of the vertex scattering. Applications of the obtained results to Josephson junction networks and DNA double helix are discussed.
THE DYNAMICS OF SINE-GORDON SYSTEM WITH DIRICHLET BOUNDARY CONDITION
Institute of Scientific and Technical Information of China (English)
Liu Yingdong; Li Zhengyuan
2000-01-01
We prove the existence of the global attractor of Sine-Gordon system with Dirichlet boundary condition and show the attractor is the unique steady state when the damping constant and the diffusion constant are sufficiently large.
Pi-kinks in a parametrically driven sine-Gordon chain
DEFF Research Database (Denmark)
Kivshar, Yuri S.; Grønbech-Jensen, Niels; Samuelsen, Mogens Rugholm
1992-01-01
We consider the sine-Gordon chain driven by a high-frequency parametric force in the presence of loss. Using an analytical approach based on the method of averaging in fast oscillations, we predict that such a parametric force may support propagation of π kinks, which are unstable in the standard...... sine-Gordon model. The steady-state velocity of the π kinks is calculated, and the analytical results are in good agreement with direct numerical simulations....
DEFF Research Database (Denmark)
Davidson, A.; Pedersen, Niels Falsig; Dueholm, B.
1985-01-01
We show some experimental results which suggest that total damping, including surface loss, plays a fundamental role in limiting the stability of high-velocity sine-Gordon solitons in real Josephson tunnel junctions.......We show some experimental results which suggest that total damping, including surface loss, plays a fundamental role in limiting the stability of high-velocity sine-Gordon solitons in real Josephson tunnel junctions....
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature
Tiegel, Alexander C.; Honecker, Andreas; Pruschke, Thomas; Ponomaryov, Alexey; Zvyagin, Sergei A.; Feyerherm, Ralf; Manmana, Salvatore R.
2016-03-01
The material copper pyrimidine dinitrate (Cu-PM) is a quasi-one-dimensional spin system described by the spin-1/2 X X Z Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. Based on numerical results obtained by the density-matrix renormalization group, exact diagonalization, and accompanying electron spin resonance (ESR) experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the low-energy description by the quantum sine-Gordon model. We find a deviation from the Lorentz invariant dispersion for the single-soliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sine-Gordon field theory, while composite boundary-bulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperature-induced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on Cu-PM over a wide range of the applied field.
Heun equation in a 5D sine-Gordon brane-world model with dilaton
Energy Technology Data Exchange (ETDEWEB)
Cunha, M.S.; Christiansen, H. [Universidade Estadual do Ceara (GFT/UECE), CE (Brazil). Grupo de Fisica Teorica
2011-07-01
Full text: In a brane-world scenario we find the propagation modes of the gauge field in a five-dimensional space-time. We adopt warping factors of the Randall-Sundrum type which are appropriate to regularize the hierarchy problem without imposing finite compactified extra dimensions. The existence and localization of gauge particles in the ordinary four-dimensional world is studied in detail on a thick brane derived out from the equations of motion of an action with a sine-Gordon potential contribution. Maxwell zero modes together with torsion effective fields are then obtained in a gravity-dilaton background inspired in close string theories. The dilaton plays a crucial role in order that the gauge field gets localized in a conformally invariant context. Kaluza-Klein massive states are also computed and, depending on certain parameters like dilaton coupling constant and asymptotic curvature, we are able to do it fully analytically. In a general approach we find that the solutions are of the Heun type. In some specific cases we can show that the Heun general solutions can be transformed into hypergeometric functions. In others, confluent Heun solutions can be transformed into simpler functions like Mathieu functions. Exact mass spectra are found in several cases. In others, we performed numerical calculations that show a well behaved phenomenology as well. In all the cases, Kaluza-Klein modes are strongly suppressed on the brane in the effective four-dimensional theory. (author)
Non-minimally coupled bulk scalar fields in sine-Gordon braneworld models
Moazzen, Masoumeh; Ghalenovi, Zahra
2017-10-01
In this paper, we investigate localization of bulk scalar fields in two types of five-dimensional braneworld models given by sine-Gordon potentials (SG). The sine-Gordon and Double sine-Gordon (DSG) branes are employed to produce different thick brane setups. In both scenarios, we include the bulk mass and non-minimally coupled terms in the global action and obtain some implications on the volcano-like potentials of the Kaluza-Klein modes associated to the corresponding Schrödinger-like equations. Also, we find that minimally and non-minimally coupled massive bulk scalar fields can be localized on SG and DSG branes if their bulk mass obeys an upper bound. Furthermore, it is shown that at the critical value of the non-minimal coupling constant the bulk scalar field cannot be localized on the branes.
Quasi-integrability in deformed sine-Gordon models and infinite towers of conserved charges
Blas, Harold
2016-01-01
We have studied the space-time symmetries of some soliton solutions of deformed sine-Gordon models in the context of the quasi-integrability concept. Considering a dual pair of anomalous Lax representations of the deformed model we compute analytically and numerically an infinite number of alternating conserved and asymptotically conserved charges through a modification of the usual techniques of integrable field theories. The charges associated to two-solitons with a definite parity under space-reflection symmetry, i.e. kink-kink (odd parity) and kink-antikink (even parity) scatterings with equal and opposite velocities, split into two infinite towers of conserved and asymptotically conserved charges. For two-solitons without definite parity under space-reflection symmetry (kink-kink and kink-antikink scatterings with unequal and opposite velocities) our numerical results show the existence of the asymptotically conserved charges only. However, we show that in the center-of-mass reference frame of the two so...
Arbitrarily large numbers of kink internal modes in inhomogeneous sine-Gordon equations
Energy Technology Data Exchange (ETDEWEB)
González, J.A., E-mail: jalbertgonz@yahoo.es [Department of Physics, Florida International University, Miami, FL 33199 (United States); Department of Natural Sciences, Miami Dade College, 627 SW 27th Ave., Miami, FL 33135 (United States); Bellorín, A., E-mail: alberto.bellorin@ucv.ve [Escuela de Física, Facultad de Ciencias, Universidad Central de Venezuela, Apartado Postal 47586, Caracas 1041-A (Venezuela, Bolivarian Republic of); García-Ñustes, M.A., E-mail: monica.garcia@pucv.cl [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059 (Chile); Guerrero, L.E., E-mail: lguerre@usb.ve [Departamento de Física, Universidad Simón Bolívar, Apartado Postal 89000, Caracas 1080-A (Venezuela, Bolivarian Republic of); Jiménez, S., E-mail: s.jimenez@upm.es [Departamento de Matemática Aplicada a las TT.II., E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, 28040-Madrid (Spain); Vázquez, L., E-mail: lvazquez@fdi.ucm.es [Departamento de Matemática Aplicada, Facultad de Informática, Universidad Complutense de Madrid, 28040-Madrid (Spain)
2017-06-28
We prove analytically the existence of an infinite number of internal (shape) modes of sine-Gordon solitons in the presence of some inhomogeneous long-range forces, provided some conditions are satisfied. - Highlights: • We have found exact kink solutions to the perturbed sine-Gordon equation. • We have been able to study analytically the kink stability problem. • A kink equilibrated by an exponentially-localized perturbation has a finite number of oscillation modes. • A sufficiently broad equilibrating perturbation supports an infinite number of soliton internal modes.
Thermal sine-Gordon system in the presence of different types of dissipation
DEFF Research Database (Denmark)
Salerno, M.; Samuelsen, Mogens Rugholm; Svensmark, Henrik
1988-01-01
The effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a αφt-βφxxt dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify that this......The effects of thermal fluctuations on solitons and phonons of the sine-Gordon system are investigated in the presence of a αφt-βφxxt dissipation. The analysis requires the assumption of a more general autocorrelation function for the noise than the one used in previous works. We verify...
Intermittent Switching between Soliton Dynamic States in a Perturbed Sine-Gordon Model
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Arley, N.; Christiansen, Peter Leth
1983-01-01
Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict the exis......Chaotic intermittency between soliton dynamic states has been found in a perturbed sine-Gordon system in the absence of an external ac driving term. The system is a model of a long Josephson oscillator with constant loss and bias current in an external magnetic field. The results predict...
On the Monge-Ampère equivalent of the sine-Gordon equation
Ferapontov, E V
1994-01-01
Surfaces of constant negative curvature in Euclidean space can be described by either the sine-Gordon equation for the angle between asymptotic directions, or a Monge-Ampère equation for the graph of the surface. We present the explicit form of the correspondence between these two integrable non-linear partial differential equations using their well-known properties in differential geometry. We find that the cotangent of the angle between asymptotic directions is directly related to the mean curvature of the surface. This is a Bäcklund-type transformation between the sine-Gordon and Monge-Ampère equations.
Abundant new travelling wave solutions for the (2 + 1)-dimensional Sine-Gordon equation
Energy Technology Data Exchange (ETDEWEB)
Li Zhu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000 (China)], E-mail: lizhu1813@163.com; Dong Huanhe [College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510 (China)
2008-07-15
Abundant new travelling wave solutions of the (2 + 1)-dimensional Sine-Gordon equation are obtained by the generalized Jacobi elliptic function method. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions.
Breather kink-antikink-pair conversion in the driven sine-Gordon system
DEFF Research Database (Denmark)
Lomdahl, P. S.; Olsen, O. H.; Samuelsen, Mogens Rugholm
1984-01-01
Breather excitations in the sine-Gordon equation influenced by constant driving forces are investigated—large driving forces cause the breather to split into a kk― (2π kink-2π antikink) pair while for small driving forces the breather excitations enter stationary modes. A perturbation method...
Sine-Gordon 2-pi-kink dynamics in the presence of small perturbations
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1983-01-01
The influence of external driving forces on the 2π-kink solution to the sine-Gordon equation is examined. The analysis is based on the approach that the solution to the problem can be divided into a 2π-kink part and a background or vacuum part. The behavior of the 2π kink depends strongly...
Internal oscillation frequencies and anharmonic effects for the double sine-Gordon kink
DEFF Research Database (Denmark)
Salerno, M.; Samuelsen, Mogens Rugholm
1989-01-01
A simple derivation of the small oscillation frequency around 4π-kink solutions of the double sine-Gordon equation is presented. Small corrections to these frequencies due to anharmonic effects are also numerically and analytically investigated. The analysis is based on energetic considerations...
Stabilization of breathers in a parametrically driven sine-Gordon system with loss
DEFF Research Database (Denmark)
Grønbech-Jensen, N.; Kivshar, Yu. S.; Samuelsen, Mogens Rugholm
1991-01-01
We demonstrate that in a parametrically driven sine-Gordon system with loss, a breather, if driven, can be maintained in a steady state at half the external frequency. In the small-amplitude limit the system is described by the effective perturbed nonlinear Schrödinger equation. For an arbitrary...
Determinant representation for a quantum correlation function of the lattice sine-Gordon model
Essler, F H L; Korepin, V E
1995-01-01
We consider a completely integrable lattice regularization of the sine--Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields.
The spectrum of boundary states in sine-Gordon model with integrable boundary conditions
Bajnok, Z; Takács, G; Tóth, G
2002-01-01
The bound state spectrum and the associated reflection factors are determined for the sine-Gordon model with arbitrary integrable boundary condition by closing the bootstrap. Comparing the symmetries of the bound state spectrum with that of the Lagrangian it is shown how one can "derive" the relationship between the UV and IR parameters conjectured earlier.
Some semi-classical issues in boundary sine-Gordon model
Kormos, M
2002-01-01
The semi-classical quantisation of the two lowest energy static solutions of boundary sine-Gordon model is considered. A relation between the Lagrangian and bootstrap parameters is established by comparing their quantum corrected energy difference and the exact one. This relation is also confirmed by studying the semi-classical limit of soliton reflections on the boundary.
A generalized exp-function method for multiwave solutions of sine-Gordon equation
Indian Academy of Sciences (India)
Sheng Zhang; Jian Wang; Au-Xue Peng; Bin Cai
2013-11-01
In this paper, the exp-function method is generalized to sine-Gordon (sG) equation and single-, double- and three-wave solutions are obtained. It is shown that the generalized exp-function method combined with appropriate anstaz may provide a straightforward, effective and alternative method for constructing multiwave solutions of some nonlinear partial differential equations.
Quantization of Sine-Gordon solitons on the circle: semiclassical vs. exact results
Pawellek, Michael
2008-01-01
We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function regularization in the integral representation. We compare the semiclassical results with exact numerical calculations in the literature and find excellent agreement even outside the plain semiclassical regime.
Belich, H; Paunov, R R
1999-01-01
By studying the {\\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.
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.
Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach
Institute of Scientific and Technical Information of China (English)
DAI Chao-Qing; ZHANG Jie-Fang
2006-01-01
In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.
Interconnection between static regimes in the LJJs described by the double sine-Gordon equation
Atanasova, P. Kh; Zemlyanaya, E. V.; Shukrinov, Yu M.
2012-11-01
The second harmonic contribution to the current-phase relation changes the properties of the static magnetic flux distributions in the long Josephson junction (LJJ) and inspires new homogenious and fluxon static states. We study stability properties and bifurcations of these static regimes within the frame of a model described by the double sine-Gordon equation. The critical curves behavior and the interconnection between different types of magnetic flux distributions are analyzed.
A Family of Interesting Exact Solutions of the Sine-Gordon Equation
Institute of Scientific and Technical Information of China (English)
HUANG De-Bin; LIU Zeng-Rong; WANG Li-Lian
2000-01-01
By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.
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...
Introduction to Supersymmetric Gauge Theories
Piguet, O
1997-01-01
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to account for the lack of exact supersymmetry in the actual world of elementary particles.
Post-Gaussian Effective Potential of Double sine-Gordon Field
Institute of Scientific and Technical Information of China (English)
CAI Wei-Ran; LOU Sen-Yue
2005-01-01
In the framework of the functional integral formalism, we calculate the effective potential of the double sine-Gordon (DsG) model up to the second order with an optimized expansion and the Coleman's normal-ordering prescription. Within the range of convergence, we make a comparison among the classicaland the effective potential of the first and second order. The numerical analysis shows that the DsG post-Gaussian EP possesses some fine global properties and makes a substantial and a concordant quantum correction to the features of the classical potential.
Determinant representation for a quantum correlation function of the lattice sine-Gordon model
Energy Technology Data Exchange (ETDEWEB)
Essler, Fabian H.L. [Department of Physics, Theoretical Physics, Oxford (United Kingdom); Frahm, Holger [Institut fuer Theoretische Physik, Universitaet Hannover, Hannover (Germany); Its, Alexander R. [Department of Mathematical Sciences, Indiana University-Purdue University at Indianapolis (IUPUI), Indianapolis, IN (United States); Korepin, Vladimir E. [Institute for Theoretical Physics, State University of New York at Stony Brook, Stony Brook, NY (United States); Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto (Japan); St. Petersburg Department of Mathematical Institute of Academy of Sciences of Russia, St. Petersburg (Russian Federation)
1997-01-07
We consider a completely integrable lattice regularization of the sine-Gordon model with discrete space and continuous time. We derive a determinant representation for a correlation function which in the continuum limit turns into the correlation function of local fields. The determinant is then embedded into a system of integrable integro-differential equations. The leading asymptotic behaviour of the correlation function is described in terms of the solution of a Riemann-Hilbert Problem (RHP) related to the system of integro-differential equations. The leading term in the asymptotical decomposition of the solution of the RHP is obtained. (author)
Ultrashort light bullets described by the two-dimensional sine-Gordon equation
Leblond, Hervé; 10.1103/PHYSREVA.81.063815
2011-01-01
By using a reductive perturbation technique applied to a two-level model, this study puts forward a generic two-dimensional sine-Gordon evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in Kerr media beyond the slowly varying envelope approximation. Direct numerical simulations show that, in contrast to the long-wave approximation, no collapse occurs, and that robust (2+1)-dimensional ultrashort light bullets may form from adequately chosen few-cycle input spatiotemporal wave forms. In contrast to the case of quadratic nonlinearity, the light bullets oscillate in both space and time and are therefore not steady-state lumps.
Energy Technology Data Exchange (ETDEWEB)
Lashkevich, Michael; Pugai, Yaroslav [Landau Institute for Theoretical Physics, 142432 Chernogolovka, Moscow Region (Russian Federation); Moscow Institute of Physics and Technology, 141707 Dolgoprudny, Moscow Region (Russian Federation)
2013-12-11
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [1]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon theory, and a new representation for conserved currents.
Travelling Wave Solutions to the m-KdV-Sine-Gordon Equation and the m-KdV-Sinh-Gordon Equation
Institute of Scientific and Technical Information of China (English)
LI Er-qiang; CHEN Jin-lan
2013-01-01
By using the function transformation and proper Sub-ODE,exact travelling wave solutions of the m-KdV-Sine-Gordon and the m-KdV-Sinh-Gordon equation are obtained,from which exact travelling wave solutions of the m-KdV equation,the Sine-Gordon equation and the Sinh-Gordon equation are derived.
Lashkevich, Michael
2013-01-01
We continue the study of form factors of descendant operators in the sinh- and sine-Gordon models in the framework of the algebraic construction proposed in [arXiv:0812.4776]. We find the algebraic construction to be related to a particular limit of the tensor product of the deformed Virasoro algebra and a suitably chosen Heisenberg algebra. To analyze the space of local operators in the framework of the form factor formalism we introduce screening operators and construct singular and cosingular vectors in the Fock spaces related to the free field realization of the obtained algebra. We show that the singular vectors are expressed in terms of the degenerate Macdonald polynomials with rectangular partitions. We study the matrix elements that contain a singular vector in one chirality and a cosingular vector in the other chirality and find them to lead to the resonance identities already known in the conformal perturbation theory. Besides, we give a new derivation of the equation of motion in the sinh-Gordon th...
Numerical simulation of the self-pumped long Josephson junction using a modified sine-Gordon model
DEFF Research Database (Denmark)
Sobolev, A.; Pankratov, A.; Mygind, Jesper
2006-01-01
We have numerically investigated the dynamics of a long Josephson junction (flux-flow oscillator) biased by a DC current in the presence of magnetic field. The study is performed in the frame of the modified sine-Gordon model, which includes the surface losses, RC-load at both FFO ends and the se......, which accounts for the presence of the superconducting gap, gives better qualitative agreement with experimental results compare to the conventional sine-Gordon model. (c) 2006 Elsevier B.V. All rights reserved....
Onset of spatiotemporal chaos in damped anharmonically driven sine-Gordon systems
Energy Technology Data Exchange (ETDEWEB)
Chacon, R. [Departamento de Fisica Aplicada, Escuela de Ingenierias Industriales, Universidad de Extremadura, E-06071, Badajoz (Spain)], E-mail: rchacon@unex.es
2008-08-15
The onset is demonstrated of spatiotemporal chaos arising from the competition between sine-Gordon-breather and kink-antikink-pair solitons by reshaping of a sinusoidal force. After introducing soliton collective coordinates, Melnikov's method is applied to the resulting effective equation of motion to deduce the parameter-space regions of the ac force where chaotic instabilities are induced. The analysis reveals that the chaotic threshold amplitude when altering solely the pulse shape presents a minimum when the transmitted impulse is maximal, the remaining parameters being held constant. The universality of the results is shown by studying the behaviour of the Lyapunov exponent from a simple recursion relation which models an unstable limit cycle. Computer simulations of the sine-Gordon system show good agreement with the theoretical predictions. Additionally, it is found that the reshaping-induced order {r_reversible} chaos route is especially rich, including transitions from a two-breather state to a spatially uniform, periodic oscillatory state. The appearance of this spatially uniform state is explained by means of geometrical resonance analysis.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Currents in supersymmetric field theories
Derendinger, Jean-Pierre
2016-01-01
A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to gauge fields. These families of supercurrent structures are characterized by their energy-momentum tensors and R currents and they display a specific relation to the dilatation current of the theory. The linear superfield is introduced in order to describe the gauge coupling as a background (or propagating) field. Supersymmetry does not constrain the dependence on this gauge coupling field of gauge kinetic terms and holomorphicity restrictions are absent. Applying these results to an effective (Wilson) description of super-Yang-Mills theory, matching or cancellation of anomalies leads to an algebraic derivation of the all-order NSVZ beta function.
SOLITONES KINK Y ANTIKENK EN LA ECUACIÓN DE SINE -GORDON
Directory of Open Access Journals (Sweden)
Francis Armando Segovia Chaves
2012-08-01
Full Text Available La ecuación de sine-Gordon es una ecuación diferencial no lineal, tiene grandes aplicaciones no solamente en la teoría de campos relativistas, sino también encuentra aplicación en la física del estado sólido y en el transporte de señales en la fibra óptica. En este trabajo se estudian dos soluciones que tiene esta ecuación diferencial como lo son las soluciones tipo solitón kink y soluciones tipo solitón antikink. Para obtener dichas soluciones se realiza el modelamiento matemático y se representa gráficamente su evolución espacio temporal.
Sine-Gordon solitons, auxiliary fields and singular limit of a double pendulums chain
Energy Technology Data Exchange (ETDEWEB)
Cadoni, Mariano [Dipartimento di Fisica, Universita di Cagliari and I.N.F.N., Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Leo, Roberto De [Dipartimento di Fisica, Universita di Cagliari and I.N.F.N., Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, via Saldini 50, 20133 Milano (Italy)
2007-10-26
We consider the continuum version of an elastic chain supporting topological and non-topological degrees of freedom; this generalizes a model for the dynamics of DNA recently proposed and investigated by ourselves. In a certain limit, the non-topological degrees of freedom are frozen, and the model reduces to the sine-Gordon equations and thus supports well-known topological soliton solutions. We consider a (singular) perturbative expansion around this limit and study in particular how the non-topological field assumes the role of an auxiliary field. This provides a more general framework for the slaving of this degree of freedom on the topological one, already observed elsewhere in the context of the mentioned DNA model; in this framework one expects such a phenomenon to arise in a quite large class of field-theoretical models.
The solution of the two-dimensional sine-Gordon equation using the method of lines
Bratsos, A. G.
2007-09-01
The method of lines is used to transform the initial/boundary-value problem associated with the two-dimensional sine-Gordon equation in two space variables into a second-order initial-value problem. The finite-difference methods are developed by replacing the matrix-exponential term in a recurrence relation with rational approximants. The resulting finite-difference methods are analyzed for local truncation error, stability and convergence. To avoid solving the nonlinear system a predictor-corrector scheme using the explicit method as predictor and the implicit as corrector is applied. Numerical solutions for cases involving the most known from the bibliography line and ring solitons are given.
Sánchez, A; Domínguez-Adame, F; Angel Sanchez; Francisco Dominguez-Adame
1994-01-01
We have examined the dynamical behavior of the kink solutions of the one-dimensional sine-Gordon equation in the presence of a spatially periodic parametric perturbation. Our study clarifies and extends the currently available knowledge on this and related nonlinear problems in four directions. First, we present the results of a numerical simulation program which are not compatible with the existence of a radiative threshold, predicted by earlier calculations. Second, we carry out a perturbative calculation which helps interpret those previous predictions, enabling us to understand in depth our numerical results. Third, we apply the collective coordinate formalism to this system and demonstrate numerically that it accurately reproduces the observed kink dynamics. Fourth, we report on a novel occurrence of length scale competition in this system and show how it can be understood by means of linear stability analysis. Finally, we conclude by summarizing the general physical framework that arises from our study.
Directory of Open Access Journals (Sweden)
Yair Zarmi
Full Text Available The (1+1-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its kink solutions (one-dimensional fronts are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these tests. Although it has been derived over the years for quite a few physical systems that have nothing to do with Special Relativity, the Sine-Gordon equation emerges as a non-linear relativistic wave equation. This opens the way for exploiting the tools of the Theory of Special Relativity. Using no more than the relativistic kinematics of tachyonic momentum vectors, from which the solutions are constructed through the Hirota algorithm, the existence and classification of N-moving-front solutions of the (1+2- and (1+3-dimensional equations for all N ≥ 1 are presented. In (1+2 dimensions, each multi-front solution propagates rigidly at one velocity. The solutions are divided into two subsets: Solutions whose velocities are lower than a limiting speed, c = 1, or are greater than or equal to c. To connect with concepts of the Theory of Special Relativity, c will be called "the speed of light." In (1+3-dimensions, multi-front solutions are characterized by spatial structure and by velocity composition. The spatial structure is either planar (rotated (1+2-dimensional solutions, or genuinely three-dimensional--branes. Planar solutions, propagate rigidly at one velocity, which is lower than, equal to, or higher than c. Branes must contain clusters of fronts whose speed exceeds c = 1. Some branes are "hybrids": different clusters of fronts propagate at different velocities. Some velocities may be lower than c but some must be equal to, or exceed, c. Finally, the speed of light cannot be approached from within the subset of slower-than-light solutions in both (1+2 and (1+3 dimensions.
Supersymmetric theories on squashed five-sphere
Imamura, Yosuke
2012-01-01
We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.
Directory of Open Access Journals (Sweden)
H. S. Shukla
2015-01-01
Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.
Sine-Gordon modulation solutions: Application to macroscopic non-lubricant friction
Gershenzon, Naum I.; Bambakidis, Gust; Skinner, Thomas E.
2016-10-01
The Frenkel-Kontorova (FK) model and its continuum approximation, the sine-Gordon (SG) equation, are widely used to model a variety of important nonlinear physical systems. Many practical applications require the wave-train solution, which includes many solitons. In such cases, an important and relevant extension of these models applies Whitham's averaging procedure to the SG equation. The resulting SG modulation equations describe the behavior of important measurable system parameters that are the average of the small-scale solutions given by the SG equation. A fundamental problem of modern physics that is the topic of this paper is the description of the transitional process from a static to a dynamic frictional regime. We have shown that the SG modulation equations are a suitable apparatus for describing this transition. The model provides relations between kinematic (rupture and slip velocities) and dynamic (shear and normal stresses) parameters of the transition process. A particular advantage of the model is its ability to describe frictional processes over a wide range of rupture and slip velocities covering seismic events ranging from regular earthquakes, with rupture velocities on the order of a few km/s, to slow slip events, with rupture velocities on the order of a few km/day.
Supersymmetric integrable scattering theories with unstable particles
Fring, A
2005-01-01
We propose scattering matrices for N=1 supersymmetric integrable quantum field theories in 1+1 dimensions which involve unstable particles in their spectra. By means of the thermodynamic Bethe ansatz we analyze the ultraviolet behaviour of some of these theories and identify the effective Virasoro central charge of the underlying conformal field theories.
New dualities of supersymmetric gauge theories
2016-01-01
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...
N=1 Supersymmetric Boundary Bootstrap
Toth, G Z
2004-01-01
We investigate the boundary bootstrap programme for finding exact reflection matrices of integrable boundary quantum field theories with N=1 boundary supersymmetry. The bulk S-matrix and the reflection matrix are assumed to take the form S=S_1S_0, R=R_1R_0, where S_0 and R_0 are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S_1 and R_1 describe the mixing of supersymmetric indices. Under the assumption that the bulk particles transform in the kink and boson/fermion representations and the ground state is a singlet we present rules by which the supersymmetry representations and reflection factors for excited boundary bound states can be determined. We apply these rules to the boundary sine-Gordon model, to the boundary a_2^(1) and a_4^(1) affine Toda field theories, to the boundary sinh-Gordon model and to the free particle.
Interaction of sine-Gordon kinks and breathers with a parity-time-symmetric defect
Saadatmand, Danial; Dmitriev, Sergey V.; Borisov, Denis I.; Kevrekidis, Panayotis G.
2014-11-01
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized parity-time-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is demonstrated that if a kink passes the defect, it always restores its initial momentum and energy, and the only effect of the interaction with the defect is a phase shift of the kink. A kink approaching the defect from the gain side always passes, while in the opposite case it must have sufficiently large initial momentum to pass through the defect instead of being trapped in the loss region. The kink phase shift and critical velocity are calculated by means of the collective variable method. Kink-kink (kink-antikink) collisions at the defect are also briefly considered, showing how their pairwise repulsive (respectively, attractive) interaction can modify the collisional outcome of a single kink within the pair with the defect. For the breather, the result of its interaction with the defect depends strongly on the breather parameters (velocity, frequency, and initial phase) and on the defect parameters. The breather can gain some energy from the defect and as a result potentially even split into a kink-antikink pair, or it can lose a part of its energy. Interestingly, the breather translational mode is very weakly affected by the dissipative perturbation, so that a breather penetrates more easily through the defect when it comes from the lossy side, than a kink. In all studied soliton-defect interactions, the energy loss to radiation of small-amplitude extended waves is negligible.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Hayashi, T; Okuyama, K; Suzuki, H; Hayashi, Takuya; Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi
1998-01-01
We formulate a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background-field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has the covariant form and can emerge only in one-loop diagrams with all the external lines are the background gauge superfield. We also present several illustrative applications in the one-loop approximation: The self-energy part of the chiral multiplet and the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and the anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Neutrino masses and mixing in supersymmetric theories
Indian Academy of Sciences (India)
Sudhir K Vempati
2000-07-01
It has been known for sometime that supersymmetric theories with -parity violation provide a natural framework where small neutrino masses can be generated. We discuss neutrino masses and mixing in these theories in the presence of trilinear lepton number violating couplings. It will be shown that simultaneous solutions to solar and atmospheric neutrino problems can be realized in these models.
Softly Broken Supersymmetric Gauge Theories through Compactifications
Takenaga, K
1998-01-01
Effects of boundary conditions of fields for compactified space directions on the supersymmetric gauge theories are discussed. For general and possible boundary conditions the supersymmetry is explicitly broken to yield universal soft supersymmetry breaking terms, and the gauge symmetry of the theory can also be broken through the dynamics of non-integrable phases, depending on number and the representation under the gauge group of matters. The 4-dimensional supersymmetric QCD is studied as a toy model when one of the space coordinates is compactified on $S^1$.
Institute of Scientific and Technical Information of China (English)
田野; 陈静; 张忠飞
2012-01-01
In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.
Renormalizable supersymmetric gauge theory in six dimensions
Energy Technology Data Exchange (ETDEWEB)
Ivanov, E.A. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: eivanov@theor.jinr.ru; Smilga, A.V. [SUBATECH, Universite de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307 (France)]. E-mail: smilga@subatech.in2p3.fr; Zupnik, B.M. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: zupnik@theor.jinr.ru
2005-10-17
We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N=(1,0) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.
Electric dipole moments in supersymmetric theories
Romanino, Andrea
1996-01-01
Intrinsic EDMs in microscopic systems at a level of sensitivity achievable in experiments under way or foreseen are predicted in supersymmetric unified theories. I describe this and other sources of measurable EDMs and I show how these sources can be distinguished through experiments in different systems.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Small numbers in supersymmetric theories of nature
Energy Technology Data Exchange (ETDEWEB)
Graesser, Michael Lawrence [Univ. of California, Berkeley, CA (United States)
1999-05-01
The Standard Model of particle interactions is a successful theory for describing the interactions of quarks, leptons and gauge bosons at microscopic distance scales. Despite these successes, the theory contains many unsatisfactory features. The origin of particle masses is a central mystery that has eluded experimental elucidation. In the Standard Model the known particles obtain their mass from the condensate of the so-called Higgs particle. Quantum corrections to the Higgs mass require an unnatural fine tuning in the Higgs mass of one part in 10^{-32} to obtain the correct mass scale of electroweak physics. In addition, the origin of the vast hierarchy between the mass scales of the electroweak and quantum gravity physics is not explained in the current theory. Supersymmetric extensions to the Standard Model are not plagued by this fine tuning issue and may therefore be relevant in Nature. In the minimal supersymmetric Standard Model there is also a natural explanation for electroweak symmetry breaking. Supersymmetric Grand Unified Theories also correctly predict a parameter of the Standard Model. This provides non-trivial indirect evidence for these theories. The most general supersymmetric extension to the Standard Model however, is excluded by many physical processes, such as rare flavor changing processes, and the non-observation of the instability of the proton. These processes provide important information about the possible structure such a theory. In particular, certain parameters in this theory must be rather small. A physics explanation for why this is the case would be desirable. It is striking that the gauge couplings of the Standard Model unify if there is supersymmetry close to the weak scale. This suggests that at high energies Nature is described by a supersymmetric Grand Unified Theory. But the mass scale of unification must be introduced into the theory since it does not coincide with the probable mass scale of strong quantum gravity
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.)
Planar Gravitational Corrections For Supersymmetric Gauge Theories
Dijkgraaf, R; Ooguri, H; Vafa, C; Zanon, D
2004-01-01
In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.
Kevrekidis, Panayotis; Williams, Floyd
2014-01-01
The sine-Gordon model is a ubiquitous model of Mathematical Physics with a wide range of applications extending from coupled torsion pendula and Josephson junction arrays to gravitational and high-energy physics models. The purpose of this book is to present a summary of recent developments in this field, incorporating both introductory background material, but also with a strong view towards modern applications, recent experiments, developments regarding the existence, stability, dynamics and asymptotics of nonlinear waves that arise in the model. This book is of particular interest to a wide range of researchers in this field, but serves as an introductory text for young researchers and students interested in the topic. The book consists of well-selected thematic chapters on diverse mathematical and physical aspects of the equation carefully chosen and assigned.
Supersymmetric black holes in string theory
Energy Technology Data Exchange (ETDEWEB)
Mohaupt, T. [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL (United Kingdom)
2007-05-15
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2 supergravity, special geometry, the black hole attractor equations and the underlying variational principle. Special attention is payed to the crucial role of higher derivative corrections. Finally we discuss black hole partition functions and their relation with the topological string, mainly from the supergravity perspective. We summarize the state of art and discuss various open questions and problems. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Shortening Anomalies in Supersymmetric Theories
Gomis, Jaume; Ooguri, Hirosi; Seiberg, Nathan; Wang, Yifan
2016-01-01
We present new anomalies in two-dimensional ${\\mathcal N} =(2, 2)$ superconformal theories. They obstruct the shortening conditions of chiral and twisted chiral multiplets at coincident points. This implies that marginal couplings cannot be promoted to background super-fields in short representations. Therefore, standard results that follow from ${\\mathcal N} =(2, 2)$ spurion analysis are invalidated. These anomalies appear only if supersymmetry is enhanced beyond ${\\mathcal N} =(2, 2)$. These anomalies explain why the conformal manifolds of the K3 and $T^4$ sigma models are not K\\"ahler and do not factorize into chiral and twisted chiral moduli spaces and why there are no ${\\mathcal N} =(2, 2)$ gauged linear sigma models that cover these conformal manifolds. We also present these results from the point of view of the Riemann curvature of conformal manifolds.
Quantum symmetries in supersymmetric Toda theories
Penati, S; Penati, Silvia; Zanon, Daniela
1992-01-01
: We consider two--dimensional supersymmetric Toda theories based on the Lie superalgebras $A(n,n)$, $D(n+1,n)$ and $B(n,n)$ which admit a fermionic set of simple roots and a fermionic untwisted affine extension. In particular, we concentrate on two simple examples, the $B(1,1)$ and $A(1,1)$ theories. Both in the conformal and massive case we address the issue of quantum integrability by constructing the first non trivial conserved currents and proving their conservation to all--loop orders. While the $D(n+1,n)$ and $B(n,n)$ systems are genuine $N=1$ supersymmetric theories, the $A(n,n)$ models possess a global $N=2$ supersymmetry. In the conformal case, we show that the $A(n,n)$ stress--energy tensor, uniquely determined by the holomorphicity condition, has vanishing central charge and it corresponds to the stress--energy tensor of the associated topological theory. (Invited talk at the International Workshop ``String theory, quantum gravity and the unification of the fundamental interactions'', Roma, Septem...
Supersymmetric Microscopic Theory of the Standard Model
Ter-Kazarian, G T
2000-01-01
We promote the microscopic theory of standard model (MSM, hep-ph/0007077) into supersymmetric framework in order to solve its technical aspects of vacuum zero point energy and hierarchy problems, and attempt, further, to develop its realistic viable minimal SUSY extension. Among other things that - the MSM provides a natural unification of geometry and the field theory, has clarified the physical conditions in which the geometry and particles come into being, in microscopic sense enables an insight to key problems of particle phenomenology and answers to some of its nagging questions - a present approach also leads to quite a new realization of the SUSY yielding a physically realistic particle spectrum. It stems from the special subquark algebra, from which the nilpotent supercharge operators are derived. The resulting theory makes plausible following testable implications for the current experiments at LEP2, at the Tevatron and at LHC drastically different from those of the conventional MSSM models: 1. All t...
Gravitational Quantum Foam and Supersymmetric Gauge Theories
Maeda, T; Noma, Y; Tamakoshi, T; Maeda, Takashi; Nakatsu, Toshio; Noma, Yui; Tamakoshi, Takeshi
2005-01-01
We study K\\"{a}hler gravity on local SU(N) geometry and describe precise correspondence with certain supersymmetric gauge theories and random plane partitions. The local geometry is discretized, via the geometric quantization, to a foam of an infinite number of gravitational quanta. We count these quanta in a relative manner by measuring a deviation of the local geometry from a singular Calabi-Yau threefold, that is a A_{N-1} singularity fibred over \\mathbb{P}^1. With such a regularization prescription, the number of the gravitational quanta becomes finite and turns to be the perturbative prepotential for five-dimensional \\mathcal{N}=1 supersymmetric SU(N) Yang-Mills. These quanta are labelled by lattice points in a certain convex polyhedron on \\mathbb{R}^3. The polyhedron becomes obtainable from a plane partition which is the ground state of a statistical model of random plane partition that describes the exact partition function for the gauge theory. Each gravitational quantum of the local geometry is shown...
Introduction to Supersymmetric Theory of Stochastics
Directory of Open Access Journals (Sweden)
Igor V. Ovchinnikov
2016-03-01
Full Text Available Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO. This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, 1/f noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS. There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful.
Effective Action of Softly Broken Supersymmetric Theories
Nibbelink, S G; Nibbelink, Stefan Groot; Nyawelo, Tino S.
2007-01-01
We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non-commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kaehler potential.
Phases of supersymmetric O(N) theories
Heilmann, Marianne; Synatschke-Czerwonka, Franziska; Wipf, Andreas
2012-01-01
We perform a global renormalization group study of O(N) symmetric Wess-Zumino theories and their phases in three euclidean dimensions. At infinite N the theory is solved exactly. The phases and phase transitions are worked out for finite and infinite short-distance cutoffs. A distinctive new feature arises at strong coupling, where the effective superfield potential becomes multi-valued, signalled by divergences in the fermion-boson interaction. Our findings resolve the long-standing puzzle about the occurrence of degenerate O(N) symmetric phases. At finite N, we find a strongly-coupled fixed point in the local potential approximation and explain its impact on the phase transition. We also examine the possibility for a supersymmetric Bardeen-Moshe-Bander phenomenon, and relate our findings with the spontaneous breaking of supersymmetry in other models.
The Supersymmetric Effective Field Theory of Inflation
Delacretaz, Luca V; Senatore, Leonardo
2016-01-01
We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable St\\"uckelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplif...
Sakhel, Asaad R.
2015-01-01
The properties of interacting bosons in a weak, one-dimensional, and bichromatic optical with a rational ratio of the constituting wavelengths $\\lambda_1$ and $\\lambda_2$ are numerically examined along a broad range of the Lieb-Liniger interaction parameter $\\gamma$ passing through the Sine-Gordon transition. It is argued that there should not be much difference in the results between those due to an irrational ratio $\\lambda_1/\\lambda_2$ and due to a rational approximation of the latter. For...
New Dualities in Supersymmetric Chiral Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Craig, Nathaniel; /Princeton, Inst. Advanced Study /Rutgers U., Piscataway; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2011-08-15
We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F {le} N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F {le} N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.
Superconformal indices and partition functions for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Gahramanov, I.B. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Humboldt-Universitaet, Berlin (Germany). Inst. fuer Physik; Vartanov, G.S. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2012-12-15
Recently there was a substantial progress in understanding of supersymmetric theories (in particular, their BPS spectrum) in space-times of different dimensions due to the exact computation of superconformal indices and partition functions using localization method. Here we discuss a connection of 4d superconformal indices and 3d partition functions using a particular example of supersymmetric theories with matter in antisymmetric representation.
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
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.
Type I integrable defects and finite-gap solutions for KdV and sine-Gordon models
Corrigan, E.; Parini, R.
2017-07-01
The main purpose of this paper is to extend results, which have been obtained previously to describe the classical scattering of solitons with integrable defects of type I, to include the much larger and intricate collection of finite-gap solutions defined in terms of generalised theta functions. In this context, it is generally not feasible to adopt a direct approach, via ansätze for the fields to either side of the defect tuned to satisfy the defect sewing conditions. Rather, essential use is made of the fact that the defect sewing conditions themselves are intimately related to Bäcklund transformations in order to set up a strategy to enable the calculation of the field on one side by suitably transforming the field on the other side. The method is implemented using Darboux transformations and illustrated in detail for the sine-Gordon and KdV models. An exception, treatable by both methods, indirect and direct, is provided by the genus 1 solutions. These can be expressed in terms of Jacobi elliptic functions, which satisfy a number of useful identities of relevance to this problem. There are new features to the solutions obtained in the finite-gap context but, in all cases, if a (multi)soliton limit is taken within the finite-gap solutions previously known results are recovered.
Non-Linear Integral Equation and excited-states scaling functions in the sine-Gordon model
Destri, C
1997-01-01
The NLIE (the non-linear integral equation equivalent to the Bethe Ansatz equations for finite size) is generalized to excited states, that is states with holes and complex roots over the antiferromagnetic ground state. We consider the sine-Gordon/massive Thirring model (sG/mT) in a periodic box of length L using the light-cone approach, in which the sG/mT model is obtained as the continuum limit of an inhomogeneous six vertex model. This NLIE is an useful starting point to compute the spectrum of excited states both analytically in the large L (perturbative) and small L (conformal) regimes as well as numerically. We derive the conformal weights of the Bethe states with holes and non-string complex roots (close and wide roots) in the UV limit. These weights agree with the Coulomb gas description, yielding a UV conformal spectrum related by duality to the IR conformal spectrum of the six vertex model.
Lorentz violation in supersymmetric field theories.
Nibbelink, Stefan Groot; Pospelov, Maxim
2005-03-04
We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric standard model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultraviolet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.
Chiral anomalies in N=1 supersymmetric Yang-Mills theories
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Grimm, R.; Stora, R. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1985-06-20
We establish a manifestly supersymmetric, compact, formula for the chiral anomalies of supersymmetric gauge theories. This result is obtained by combining superspace geometry with the usual algebra of anomalies. Except for a Wess-Zumino type term, we obtain an expression which is polynomial in the coefficients of the superconnection form.
Supersymmetric M5 brane theories on R × CP2
Kim, Hee-Cheol; Lee, Kimyeong
2013-07-01
We propose 4 and 12 supersymmetric conformal Yang-Mills-Chern-Simons theories on R × CP2 as multiple representations of the theory on M5 branes. These theories are obtained by twisted Zk modding and dimensional reduction of the 6d (2,0) superconformal field theory on R × S5 and have a discrete coupling constant 1/{g_{{YM}^2}}=k/{4{π^2}} with natural number k. Instantons in these theories are expected to represent the Kaluza-Klein modes. For the k = 1 , 2 cases, we argue that the number of supersymmetries in our theories should be enhanced to 32 and 16, respectively. For the k = 3 case, only the 4 supersymmetric theory gets the supersymmetric enhancement to 8. For the 4 supersymmetric case, the vacuum structure becomes more complicated as there are degenerate supersymmetric vacua characterized by fuzzy spheres. We calculate the perturbative part of the SU( N ) gauge group Euclidean path integral for the index function at the symmetric phase of the 4 supersymmetric case and confirm it with the known half-BPS index. From the similar twisted Z k modding of the AdS7 × S4 geometry, we speculate that the M region is for k ≲ N 1/3 and the type IIA region is N 1/3 ≲ k ≲ N. When nonperturbative corrections are included, our theories are expected to produce the full index of the 6d (2,0) theory.
Aspects of a supersymmetric Brans-Dicke theory
Energy Technology Data Exchange (ETDEWEB)
Catena, R.
2006-11-15
We consider a locally supersymmetric theory where the Planck mass is replaced by a dynamical superfield. This model can be thought of as the Minimal Supersymmetric extension of the Brans-Dicke theory (MSBD). The motivation that underlies this analysis is the research of possible connections between Dark Energy models based on Brans-Dicke-like theories and supersymmetric Dark Matter scenarios. We find that the phenomenology associated with the MSBD model is very different compared to the one of the original Brans-Dicke theory: the new scalar and fermionic degrees of freedom do not couple to matter in a universal metric way, i.e. they can not be removed from the matter sector by a Weyl rescaling of the metric. This feature could make the minimal supersymmetric extension of the BD idea phenomenologically inconsistent. (orig.)
Simulations of supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Demmouche, K.; Farchioni, F.; Ferling, A.; Muenster, G.; Wuilloud, J. [Muenster Univ. (Germany); Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Scholz, E.E. [Fermi National Accelerator Lab., Batavia, IL (United States)
2009-11-15
Results of a numerical simulation concerning the low-lying spectrum of four-dimensional N = 1 SU(2) Supersymmetric Yang-Mills (SYM) theory on the lattice with light dynamical gluinos are reported. We use the tree-level Symanzik improved gauge action and Wilson fermions with stout smearing of the gauge links in the Wilson-Dirac operator. The configurations are produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) algorithm. We performed simulations on lattices up to a size of 24{sup 3}.48 at {beta}=1.6. Using QCD units with the Sommer scale being set to r{sub 0}=0.5 fm, the lattice spacing is about a {approx_equal}0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm to control finite size effects. At the lightest simulated gluino mass our results indicate a mass for the lightest gluino-glue bound state, which is considerably heavier than the values obtained for its possible superpartners. Whether supermultiplets are formed remains to be studied in upcoming simulations. (orig.)
A renormalization in group study of supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Heilmann, Marianne
2015-05-13
This thesis analyses scalar supersymmetric field theories within the framework of the functional renormalization group (FRG). Classical physics on microscopic scales is connected to the effective model on macroscopic scales via the scale-dependent effective average action by a reformulation of the path integral. Three supersymmetric theories are explored in detail: supersymmetric quantum mechanics, the three-dimensional Wess-Zumino model and supersymmetric spherical theories in three dimensions. The corresponding renormalization group flow is formulated in a manifestly supersymmetric way. By utilizing an expansion of the effective average action in derivative operators, an adequate and intrinsically non-perturbative truncation scheme is selected. In quantum mechanics, the supersymmetric derivative expansion is shown to converge by increasing the order of truncation. Besides, high-accuracy results for the ground and first excited state energies for quantum systems with conserved as well as spontaneously broken supersymmetry are achieved. Furthermore, the critical behaviour of the three-dimensional Wess-Zumino is investigated. Via spectral methods, a global Wilson-Fisher scaling solution and its corresponding universal exponents are determined. Besides, a superscaling relation of the leading exponents is verified for arbitrary dimensions greater than or equal to two. Lastly, three-dimensional spherical, supersymmetric theories are analysed. Their phase structure is determined in detail for infinite as well as finitely many superfields. The exact one-parameter scaling solution for infinitely many fields is shown to collapse to a single non-trivial Wilson-Fisher fixed-point for finitely many superfields. It is pointed out that the strongly-coupled domains of these theories are plagued by Landau poles and non-analyticities, indicating spontaneous supersymmetry breaking.
Resurgent Analysis of Localizable Observables in Supersymmetric Gauge Theories
Aniceto, Inês; Schiappa, Ricardo
2015-01-01
Localization methods have recently led to a plethora of new exact results in supersymmetric gauge theories, as certain observables may be computed in terms of matrix integrals. These can then be evaluated by making use of standard large N techniques, or else via perturbative expansions in the gauge coupling. Either approximation often leads to observables given in terms of asymptotic series, which need to be properly defined in order to obtain nonperturbative results. At the same time, resurgent analysis has recently been successfully applied to several problems, e.g., in quantum, field and string theories, precisely to overcome this issue and construct nonperturbative answers out of asymptotic perturbative expansions. The present work uses exact results from supersymmetric localization to address the resurgent structure of the free energy and partition function of Chern-Simons and ABJM gauge theories in three dimensions, and of N=2 supersymmetric Yang-Mills theories in four dimensions. For each case, the com...
Comments on twisted indices in 3d supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Closset, Cyril [Simons Center for Geometry and PhysicsState University of New York, Stony Brook, NY 11794 (United States); Kim, Heeyeon [Perimeter Institute for Theoretical Physics31 Caroline Street North, Waterloo, N2L 2Y5, Ontario (Canada)
2016-08-09
We study three-dimensional N=2 supersymmetric gauge theories on Σ{sub g}×S{sup 1} with a topological twist along Σ{sub g}, a genus-g Riemann surface. The twisted supersymmetric index at genus g and the correlation functions of half-BPS loop operators on S{sup 1} can be computed exactly by supersymmetric localization. For g=1, this gives a simple UV computation of the 3d Witten index. Twisted indices provide us with a clean derivation of the quantum algebra of supersymmetric Wilson loops, for any Yang-Mills-Chern-Simons-matter theory, in terms of the associated Bethe equations for the theory on ℝ{sup 2}×S{sup 1}. This also provides a powerful and simple tool to study 3d N=2 Seiberg dualities. Finally, we study A- and B-twisted indices for N=4 supersymmetric gauge theories, which turns out to be very useful for quantitative studies of three-dimensional mirror symmetry. We also briefly comment on a relation between the S{sup 2}×S{sup 1} twisted indices and the Hilbert series of N=4 moduli spaces.
Two-loop beta functions for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Jack, I. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)
1984-11-15
The two-loop ..beta.. functions in the dimensional regularisation framework for a general gauge theory coupled to scalar and spinor fields are presented and by means of a finite transformation of the couplings are converted into a form which vanishes for special cases corresponding to supersymmetric gauge theories.
Deformed supersymmetric gauge theories from the fluxtrap background
Orlando, Domenico
2013-01-01
The fluxtrap background of string theory provides a transparent and algorithmic way of constructing supersymmetric gauge theories with both mass and Omega-type deformations in various dimensions. In this article, we review a number of deformed supersymmetric gauge theories in two and four dimensions which can be obtained via the fluxtrap background from string or M-theory. Such theories, the most well-known being Omega-deformed super Yang-Mills theory in four dimensions, have met with a lot of interest in the recent literature. The string theory treatment offers many new avenues of analysis and applications, such as for example the study of the gravity duals for deformed N=4 gauge theories.
Stable Non-Supersymmetric Throats in String Theory
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit; Simic, Dusan; /Stanford U., ITP /SLAC /Santa Barbara, KITP; Trivedi, Sandip P.; /Tata Inst. /Stanford U., ITP /SLAC
2011-06-28
We construct a large class of non-supersymmetric AdS-like throat geometries in string theory by taking non-supersymmetric orbifolds of supersymmetric backgrounds. The scale of SUSY breaking is the AdS radius, and the dual field theory has explicitly broken supersymmetry. The large hierarchy of energy scales in these geometries is stable. We establish this by showing that the dual gauge theories do not have any relevant operators which are singlets under the global symmetries. When the geometries are embedded in a compact internal space, a large enough discrete subgroup of the global symmetries can still survive to prevent any singlet relevant operators from arising. We illustrate this by embedding one case in a non-supersymmetric orbifold of a Calabi-Yau manifold. These examples can serve as a starting point for obtaining Randall-Sundrum models in string theory, and more generally for constructing composite Higgs or technicolor-like models where strongly coupled dynamics leads to the breaking of electro-weak symmetry. Towards the end of the paper, we briefly discuss how bulk gauge fields can be incorporated by introducing D7-branes in the bulk, and also show how the strongly coupled dynamics can lead to an emergent weakly coupled gauge theory in the IR with matter fields including scalars.
Exact half-BPS type IIB interface solutions I: local solution and supersymmetric Janus
Energy Technology Data Exchange (ETDEWEB)
D' Hoker, Eric; Estes, John; Gutperle, Michael [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)
2007-06-15
The complete Type IIB supergravity solutions with 16 supersymmetries are obtained on the manifold AdS{sub 4} x S{sup 2} x S{sup 2} x {sigma} with SO(2, 3) x SO(3) x SO(3) symmetry in terms of two holomorphic functions on a Riemann surface {sigma}, which generally has a boundary. This is achieved by reducing the BPS equations using the above symmetry requirements, proving that all solutions of the BPS equations solve the full Type IIB supergravity field equations, mapping the BPS equations onto a new integrable system akin to the Liouville and Sine-Gordon theories, and mapping this integrable system to a linear equation which can be solved exactly. Amongst the infinite class of solutions, a non-singular Janus solution is identified which provides the AdS/CFT dual of the maximally supersymmetric Yang-Mills interface theory discovered recently. The construction of general classes of globally non-singular solutions, including fully back-reacted AdS{sub 5} x S{sup 5} and supersymmetric Janus doped with D5 and/or NS5 branes, is deferred to a companion paper.
An introduction to supersymmetric field theories in curved space
Dumitrescu, Thomas T
2016-01-01
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.
From Scalar Field Theories to Supersymmetric Quantum Mechanics
Bazeia, D
2016-01-01
In this work we report a new result that appears when one investigates the route that starts from a scalar field theory and ends on a supersymmetric quantum mechanics. The subject has been studied before in several distinct ways and here we unveil an interesting novelty, showing that the same scalar field model may describe distinct quantum mechanical problems.
Comments on the spontaneous symmetry breaking in supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Sorba, P.; Stora, R. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1984-08-30
The role of the complex extension of the symmetry group in supersymmetric theories is revisited. We prove, in particular, that if symmetry breaking occurs at an extremum of the superpotential, then supersymmetry will be preserved if and only if the complex stabilizer of the vacuum is the complexified of its maximal compact part.
Invariant Regularization of Supersymmetric Chiral Gauge Theory, 2
Hayashi, T; Okuyama, K; Suzuki, H; Hayashi, Takuya; Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi
1998-01-01
By supplementing additional analyses postponed in the previous paper, we complete our construction of manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. We present: An evaluation of the covariant gauge anomaly; the proof of integrability of the covariant gauge current in anomaly-free cases; a calculation of one-loop superconformal anomaly in the gauge supermultiplet sector. On the last point, we find that the ghost-anti-ghost supermultiplet and the Nakanishi-Lautrup supermultiplet give rise to BRST exact contributions which, due to the Slavnov-Taylor identities in our regularization scheme, can safely be neglected.
Global Properties of Supersymmetric Theories and the Lens Space
Razamat, Shlomo S
2013-01-01
We compute the supersymmetric partition function on L(r,1)xS^1, the lens space index, for 4d gauge theories related by supersymmetric dualities and involving non simply-connected groups. This computation is sensitive to the global properties of the underlying gauge group and to discrete theta angle parameters and thus distinguishes versions of dualities differing by such. We explicitly discuss N=1 so(N_c) Seiberg dualities and N=4 su(N_c) S-dualities.
Higher Derivative Corrections To Extended Supersymmetric Theories
Braun, G A
2004-01-01
We investigate higher-derivative terms in N = 2 supersymmetric effective actions. We systematically construct such terms in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. We write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches, modulo the existence of superspace Chern-Simons-like terms. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. We then search for superspace Chern-Simons-like terms, which are those gauge-invariant terms which cannot be written solely in terms of field strength superfields and covariant derivatives, but in which gauge potential superfield appears explicitly. We find a class of four- derivative terms with N = 2 supersymmetry which, though locally on the Coulomb branch can be written solely in terms of field strengths, globally on the Coulomb branch are superspace Chern- Simons-like.
Chakraborty, Debananda
2011-01-01
We consider the Klein-Gordon and sine-Gordon type equations with a point-like potential, which describes the wave phenomenon in disordered media with a defect. The singular potential term yields a critical phenomenon--that is, the solution behavior around the critical parameter value bifurcates into two extreme cases. Pinpointing the critical value with arbitrary accuracy is even more challenging. In this work, we adopt the generalized polynomial chaos (gPC) method to determine the critical values and the mean solutions around such values. First, we consider the critical value associated with the strength of the singular potential for the Klein-Gordon equation. We expand the solution in the random variable associated with the parameter. The obtained partial differential equations are solved using the Chebyshev collocation method. Due to the existence of the singularity, the Gibbs phenomenon appears in the solution, yielding a slow convergence of the numerically computed critical value. To deal with the singul...
Regge trajectories in {N} = 2 supersymmetric Yang-Mills theory
Córdova, Clay
2016-09-01
We demonstrate that {N} = 2 supersymmetric non-Abelian gauge theories have towers of BPS particles obeying a Regge relation, J ˜ m 2, between their angular momenta, J, and their masses, m. For SU( N) Yang-Mills theories, we estimate the slope of these Regge trajectories using a non-relativistic quiver quantum mechanics model. Along the way, we also prove various structure theorems for the quiver moduli spaces that appear in the calculation.
Supersymmetric Gödel Universes in string theory
DEFF Research Database (Denmark)
Harmark, Troels; Takayanagi, Tadashi
2003-01-01
Supersymmetric backgrounds in string and M-theory of the Gödel Universe type are studied. We find several new Gödel Universes that preserve up to 20 supersymmetries. In particular, we obtain an interesting Gödel Universe in M-theory with 18 supersymmetries which does not seem to be dual to a pp......-wave. We show that not only T-duality but also the type-IIA/M-theory S-duality can give supersymmetric Gödel Universes from pp-waves. We find solutions that can interpolate between Gödel Universes and pp-waves. We also compute the string spectrum on two type IIA Gödel Universes. Furthermore, we obtain...
Supersymmetric Gödel Universes in string theory
DEFF Research Database (Denmark)
Harmark, Troels; Takayanagi, Tadashi
2003-01-01
Supersymmetric backgrounds in string and M-theory of the Gödel Universe type are studied. We find several new Gödel Universes that preserve up to 20 supersymmetries. In particular, we obtain an interesting Gödel Universe in M-theory with 18 supersymmetries which does not seem to be dual to a pp......-wave. We show that not only T-duality but also the type-IIA/M-theory S-duality can give supersymmetric Gödel Universes from pp-waves. We find solutions that can interpolate between Gödel Universes and pp-waves. We also compute the string spectrum on two type IIA Gödel Universes. Furthermore, we obtain...
Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2015-01-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Quantum cohomology and quantum hydrodynamics from supersymmetric quiver gauge theories
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2016-11-01
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum cohomology of the corresponding Nakajima's quiver varieties. We also discuss how the exact evaluation of local BPS observables in the gauge theory can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero integrable systems and spin Intermediate Long Wave hydrodynamics. This is explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge theory in terms of its adjacency matrix.
Four dimensional supersymmetric theories in presence of a boundary
Directory of Open Access Journals (Sweden)
Mir Faizal
2015-09-01
Full Text Available In this paper, we study N=1 supersymmetric theories in four dimensions in presence of a boundary. We demonstrate that it is possible to preserve half the supersymmetry of the original theory by suitably modifying it in presence of a boundary. This is done by adding new boundary terms to the original action, such that the supersymmetric variation of the new terms exactly cancels the boundary terms generated by the supersymmetric transformation of the original bulk action. We also analyze the boundary projections of such supercharges used in such a theory. We study super-Yang–Mills theories in presence of a boundary using these results. Finally, we study the Born–Infeld action in presence of a boundary. We analyze the boundary effects for the Born–Infeld action coupled to a background dilaton and an axion field. We also analyze the boundary effects for a non-abelian Born–Infeld action. We explicitly construct the actions for these systems in presence of a boundary. This action preserves half of the original supersymmetry.
Supersymmetric Theory of Stochastic ABC Model: A Numerical Study
Ovchinnikov, Igor V; Ensslin, Torsten A; Wang, Kang L
2016-01-01
In this paper, we investigate numerically the stochastic ABC model, a toy model in the theory of astrophysical kinematic dynamos, within the recently proposed supersymmetric theory of stochastics (STS). STS characterises stochastic differential equations (SDEs) by the spectrum of the stochastic evolution operator (SEO) on elements of the exterior algebra or differentials forms over the system's phase space, X. STS can thereby classify SDEs as chaotic or non-chaotic by identifying the phenomenon of stochastic chaos with the spontaneously broken topological supersymmetry that all SDEs possess. We demonstrate the following three properties of the SEO, deduced previously analytically and from physical arguments: the SEO spectra for zeroth and top degree forms never break topological supersymmetry, all SDEs possesses pseudo-time-reversal symmetry, and each de Rahm cohomology class provides one supersymmetric eigenstate. Our results also suggests that the SEO spectra for forms of complementary degrees, i.e., k and ...
Higher-Rank Supersymmetric Models and Topological Field Theory
Kawai, T; Yang, S K; Kawai, Toshiya; Uchino, Taku; Yang, Sung-Kil
1993-01-01
In the first part of this paper we investigate the operator aspect of higher-rank supersymmetric model which is introduced as a Lie theoretic extension of the $N=2$ minimal model with the simplest case $su(2)$ corresponding to the $N=2$ minimal model. In particular we identify the analogs of chirality conditions and chiral ring. In the second part we construct a class of topological conformal field theories starting with this higher-rank supersymmetric model. We show the BRST-exactness of the twisted stress-energy tensor, find out physical observables and discuss how to make their correlation functions. It is emphasized that in the case of $su(2)$ the topological field theory constructed in this paper is distinct from the one obtained by twisting the $N=2$ minimal model through the usual procedure.
Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance
Dine, Michael; Haber, Howard E; Haskins, Laurel Stephenson
2016-01-01
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Cluster-like coordinates in supersymmetric quantum field theory.
Neitzke, Andrew
2014-07-08
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
Flavor violation in supersymmetric theories with gauged flavor symmetries
Kobayashi, Tatsuo; Nakano, Hiroaki; Terao, Haruhiko; Yoshioka, Koichi
2002-01-01
In this paper we study flavor violation in supersymmetric models with gauged flavor symmetries. There are several sources of flavor violation in these theories. The dominant flavor violation is the tree-level $D$-term contribution to scalar masses generated by flavor symmetry breaking. We present a new approach for suppressing this phenomenologically dangerous effects by separating the flavor-breaking sector from supersymmetry-breaking one. The separation can be achieved in geometrical setups...
BPS Boojums in N=2 supersymmetric gauge theories II
Arai, Masato; Blaschke, Filip; Eto, Minoru(Department of Physics, Yamagata University, Yamagata, 990-8560, Japan)
2016-01-01
We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in N=2 supersymmetric Abelian gauge theories in four dimensions. In this work, we numerically confirm that a boojum appearing at an end point of a string on a thick domain wall behaves as a magnetic monopole with a fractional charge in three dimensions. We introduce a "magnetic" scalar potential whose gradient gives magnetic fields. Height of the magnetic potential ...
Review of localization for 5d supersymmetric gauge theories
Qiu, Jian
2016-01-01
We give a pedagogical review of the localization of supersymmetric gauge theory on 5d toric Sasaki-Einstein manifolds. We construct the cohomological complex resulting from supersymmetry and consider its natural toric deformations with all equivariant parameters turned on. We also give detailed discussion on how the Sasaki-Einstein geometry permeates every aspect of the calculation, from Killing spinor, vanishing theorems to the index theorems.
Matrix models, topological strings, and supersymmetric gauge theories
Dijkgraaf, Robbert; Vafa, Cumrun
2002-11-01
We show that B-model topological strings on local Calabi-Yau threefolds are large- N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover ( p, q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
N=2 supersymmetric gauge theories and quantum integrable systems
Energy Technology Data Exchange (ETDEWEB)
Luo, Yuan; Tan, Meng-Chwan [Department of Physics, National University of Singapore 2 Science Drive 3, 117551 (Singapore); Yagi, Junya [Department of Physics, National University of Singapore 2 Science Drive 3, 117551 (Singapore); International School for Advanced Studies (SISSA) Via Bonomea, 265, 34136 Trieste (Italy); INFN, Sezione di Trieste Via Valerio, 2, 34149 Trieste (Italy)
2014-03-20
We study N=2 supersymmetric gauge theories on the product of a two-sphere and a cylinder. We show that the low-energy dynamics of a BPS sector of such a theory is described by a quantum integrable system, with the Planck constant set by the inverse of the radius of the sphere. If the sphere is replaced with a hemisphere, then our system reduces to an integrable system of the type studied by Nekrasov and Shatashvili. In this case we establish a correspondence between the effective prepotential of the gauge theory and the Yang-Yang function of the integrable system.
On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
Koroteev, Peter
2016-01-01
In this note we further develop the duality between supersymmetric gauge theories in various dimensions and elliptic integrable systems such as Ruijsenaars-Schneider model and periodic intermediate long wave hydrodynamics. These models arise in instanton counting problems and are described by certain elliptic algebras. We discuss the correspondence between the two types of models by employing the large-n limit of the dual gauge theory. In particular we provide non-Abelian generalization of our previous result on the intermediate long wave model.
The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
Tong, David
2015-01-01
In d=2+1 dimensions, there exist gauge theories which are supersymmetric but non-relativistic. We solve the simplest U(1) gauge theory in this class and show that the low-energy physics is that of the fractional quantum Hall effect, with ground states given by the Laughlin wavefunctions. We do this by quantising the vortices and relating them to the quantum Hall matrix model. We further construct coherent state representations of the excitations of vortices. These are quasi-holes. By an explicit computation of the Berry phase, without resorting to a plasma analogy, we show that these excitations have fractional charge and spin.
Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions
Noma, Y
2006-01-01
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov's partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model we reproduce the polyhedron which characterizes the Hilbert space.
Duality and Superconvergence Relation in Supersymmetric Gauge Theories
Tachibana, M
1998-01-01
We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.
Symplectic Deformations of Integrable Field Theories and AdS/CFT
Hollowood, Timothy J
2014-01-01
Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS(5)xS(5).
Symplectic deformations of integrable field theories and AdS/CFT
Energy Technology Data Exchange (ETDEWEB)
Hollowood, Timothy J., E-mail: t.hollowood@swansea.ac.uk [Department of Physics, Swansea University, Swansea, SA2 8PP (United Kingdom); Miramontes, J. Luis, E-mail: jluis.miramontes@usc.es [Departamento de Física de Partículas and IGFAE, Universidad de Santiago de Compostela, 15782 Santiago de Compostela (Spain)
2014-12-12
Relativistic integrable field theories like the sine-Gordon equation have an infinite set of conserved charges. In a light-front formalism these conserved charges are closely related to the integrable modified KdV hierarchy at the classical level. The latter hierarchy admits a family of symplectic structures which we argue can be viewed as deformations of the relativistic sine-Gordon symplectic structure. These deformed theories are integrable but no longer relativistic and the basic excitations of the theory, the solitons, have an interesting non-relativistic dispersion relation that in a certain limit becomes the dispersion relation of dyonic giant magnons of string theory in the AdS/CFT correspondence. We argue that the deformed classical theories can be lifted to quantum theories when the sine-Gordon theory is embedded in a larger theory that describes the string world-sheet sigma model in AdS{sub 5}×S{sup 5}.
Deconstruction and other approaches to supersymmetric lattice field theories
Giedt, J
2006-01-01
This report contains both a review of recent approaches to supersymmetric lattice field theories and some new results on the deconstruction approach. The essential reason for the complex phase problem of the fermion determinant is shown to be derivative interactions that are not present in the continuum. These irrelevant operators violate the self-conjugacy of the fermion action that is present in the continuum. It is explained why this complex phase problem does not disappear in the continuum limit. The fermion determinant suppression of various branches of the classical moduli space is explored, and found to be supportive of previous claims regarding the continuum limit.
Supersymmetric action of multiple D0-branes from matrix theory
Energy Technology Data Exchange (ETDEWEB)
Asano, Masako E-mail: asano@post.kek.jp; Sekino, Yasuhiro E-mail: sekino@th.phys.titech.ac.jp
2002-11-11
We study one-loop effective action of Berkooz-Douglas matrix theory and obtain non-Abelian action of D0-branes in the longitudinal 5-brane background. In this paper, we extend the analysis of hep-th/0201248 and calculate the part of the effective action containing fermions. We show that the effective action is manifestly invariant under the loop-corrected SUSY transformation, and give the explicit transformation laws. The effective action consists of blocks which are closed under the SUSY, and it includes the supersymmetric completion of the couplings to the longitudinal 5-branes proposed by Taylor and Van Raamsdonk as a subset.
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
D'Hoker, Eric; Phong, D. H.
Introduction Supersymmetry and the Standard Model Supersymmetry and Unification of Forces Supersymmetric Yang-Mills Dynamics Supersymmetric Yang-Mills in 4 Dimensions Supersymmetry Algebra Massless Particle Representations Massive Particle Representations Field Contents of Supersymmetric Field Theories N = 1 Supersymmetric Lagrangians N = 1 Superfield Methods Irreducible Superfields of N = 1 General N = 1 Susy Lagrangians via Superfields Renormalizable N = 2,4 Susy Lagrangians N = 2 Superfield Methods: Unconstrained Superspace N = 2 Superfield Methods: Harmonic/Analytic Superspaces Seiberg-Witten Theory Wilson Effective Couplings and Actions Holomorphicity and Nonrenormalization Low Energy Dynamics of N = 2 Super-Yang-Mills Particle and Field Contents Form of the N = 2 Low Energy Effective Lagrangian Physical Properties of the Prepotential Electric-Magnetic Duality Monodromy via Elliptic Curves for SU(2) Gauge Group Physical Interpretation of Singularities Hypergeometric Function Representation More General Gauge Groups, Hypermultiplets Model of Riemann Surfaces Identifying Seiberg-Witten and Riemann Surface Data SU(N) Gauge Algebras, Fundamental Hypermultiplets Classical Gauge Algebras, Fundamental Hypermultiplets Mechanical Integrable Systems Lax Pairs with Spectral Parameter-Spectral Curves The Toda Systems The Calogero-Moser Systems for SU(N) Relation between Calogero-Moser and Toda for SU(N) Relations with KdV and KP Systems Calogero-Moser Systems for General Lie Algebras Scaling of Calogero-Moser to Toda for General Lie Algebras Calogero-Moser Lax Pairs for General Lie Algebras Lax Pairs with Spectral Parameter for Classical Lie Algebras The General Ansatz Lax Pairs for Untwisted Calogero-Moser Systems Lax Pairs for Twisted Calogero-Moser Systems Scaling Limits of Lax Pairs Super-Yang-Mills and Calogero-Moser Systems Correspondence of Seiberg-Witten and Integrable Systems Calogero-Moser and Seiberg-Witten Theory for SU(N) Four Fundamental Theorems Partial
Dualities and Curved Space Partition Functions of Supersymmetric Theories
Agarwal, Prarit
In this dissertation we discuss some conjectured dualities in supersymmetric field theories and provide non-trivial checks for these conjectures. A quick review of supersymmetry and related topics is provided in chapter 1. In chapter 2, we develop a method to identify the so called BPS states in the Hilbert space of a supersymmetric field theory (that preserves at least two real supercharges) on a generic curved space. As an application we obtain the superconformal index (SCI) of 4d theories. The large N SCI of quiver gauge theories has been previously noticed to factorize over the set of extremal BPS mesonic operators. In chapter 3, we reformulate this factorization in terms of the zigzag paths in the dimer model associated to the quiver and extend the factorization theorem of the index to include theories obtained from D-branes probing orbifold singularities. In chapter 4, we consider the dualities in two classes of 3 dimensional theories. The first class consist of dualities of certain necklace type Chern-Simons (CS) quiver gauge theories. A non trivial check of these dualities is provided by matching their squashed sphere partition functions. The second class consists of theories whose duals are described by a collection of free fields. In such cases, due to mixing between the superconformal R-symmetry and accidental symmetries, the matching of electric and magnetic partition functions is not straightforward. We provide a prescription to rectify this mismatch. In chapter 5, we consider some the N = 1 4d theories with orthogonal and symplectic gauge groups, arising from N = 1 preserving reduction of 6d theories on a Riemann surface. This construction allows us to dual descriptions of 4d theories. Some of the dual frames have no known Lagrangian description. We check the dualities by computing the anomaly coefficients and the superconformal indices. We also give a prescription to write the index of the theory obtained by reduction of 6d theories on a three
Large N Strong Coupling Dynamics in Non-Supersymmetric Orbifold Field Theories
Dijkgraaf, R; Vafa, C; Dijkgraaf, Robbert; Neitzke, Andrew; Vafa, Cumrun
2002-01-01
We give a recipe relating holomorphic quantities in supersymmetric field theory to their descendants in non-supersymmetric Z_2 orbifold field theories. This recipe, consistent with a recent proposal of Strassler, gives exact results for bifermion condensates, domain wall tensions and gauge coupling constants in the planar limit of the orbifold theories.
Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
Dijkgraaf, R; Dijkgraaf, Robbert; Vafa, Cumrun
2002-01-01
We show that B-model topological strings on local Calabi-Yau threefolds are large N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Matrix models, topological strings, and supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert E-mail: rhd@science.uva.nl; Vafa, Cumrun
2002-11-11
We show that B-model topological strings on local Calabi-Yau threefolds are large-N duals of matrix models, which in the planar limit naturally give rise to special geometry. These matrix models directly compute F-terms in an associated N=1 supersymmetric gauge theory, obtained by deforming N=2 theories by a superpotential term that can be directly identified with the potential of the matrix model. Moreover by tuning some of the parameters of the geometry in a double scaling limit we recover (p,q) conformal minimal models coupled to 2d gravity, thereby relating non-critical string theories to type II superstrings on Calabi-Yau backgrounds.
Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
Pestun, Vasily
2007-01-01
We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the N=4 supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure N=2 and the N=2* supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional N=2 superconformal gauge theory is treated similarly.
Energy Technology Data Exchange (ETDEWEB)
Metzger, St
2005-12-15
This thesis presents various ways to construct four-dimensional quantum field theories from string theory. In a first part we study the generation of a supersymmetric Yang-Mills theory, coupled to an adjoint chiral superfield, from type IIB string theory on non-compact Calabi-Yau manifolds, with D-branes wrapping certain sub-cycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. Even if the Calabi-Yau geometry is too complicated to evaluate the geometric integrals explicitly, one can then always use matrix model perturbation theory to calculate the effective superpotential. The second part of this work covers the generation of four-dimensional super-symmetric gauge theories, carrying several important characteristic features of the standard model, from compactifications of eleven-dimensional supergravity on G{sub 2}-manifolds. If the latter contain conical singularities, chiral fermions are present in the four-dimensional gauge theory, which potentially lead to anomalies. We show that, locally at each singularity, these anomalies are cancelled by the non-invariance of the classical action through a mechanism called 'anomaly inflow'. Unfortunately, no explicit metric of a compact G{sub 2}-manifold is known. Here we construct families of metrics on compact weak G{sub 2}-manifolds, which contain two conical singularities. Weak G{sub 2}-manifolds have properties that are similar to the ones of proper G{sub 2}-manifolds, and hence the explicit examples might be useful to better understand the generic situation. Finally, we reconsider the relation between eleven-dimensional supergravity and the E{sub 8} x E{sub 8}-heterotic string. This is done by carefully studying the anomalies that appear if the supergravity theory is formulated on a ten-manifold times the interval. Again we find that the anomalies cancel locally at the boundaries of the interval through anomaly inflow, provided one suitably modifies the
Supersymmetric Yang-Mills theory as higher Chern-Simons theory
Sämann, Christian; Wolf, Martin
2017-07-01
We observe that the string field theory actions for the topological sigma models describe higher or categorified Chern-Simons theories. These theories yield dynamical equations for connective structures on higher principal bundles. As a special case, we consider holomorphic higher Chern-Simons theory on the ambitwistor space of four-dimensional space-time. In particular, we propose a higher ambitwistor space action functional for maximally supersymmetric Yang-Mills theory.
Supersymmetric gauge theories, intersecting branes and free fermions
Dijkgraaf, Robbert; Hollands, Lotte; Sułkowski, Piotr; Vafa, Cumrun
2008-02-01
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.
Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions
Dijkgraaf, Robbert; Sulkowski, Piotr; Vafa, Cumrun
2008-01-01
We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.
Integrable structure in supersymmetric gauge theories with massive hypermultiplets
Ahn, C; Ahn, Changhyun; Nam, Soonkeon
1996-01-01
We study the quantum moduli space of vacua of N=2 supersymmetric SU(N_c) gauge theories coupled to N_f flavors of quarks in the fundamental representation. We identify the moduli space of the N_c = 3 and N_f=2 massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with {\\it massive} quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of N_{c}=3 with N_{f}=0, 1, 2. We discuss possible generalizations of the integrable systems relevant to gauge theories with N_c \
Local gauge coupling running in supersymmetric gauge theories on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Hillenbach, M.
2007-11-21
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
Directory of Open Access Journals (Sweden)
E. Ireson
2016-01-01
Full Text Available In this work we extend the results of previous derivations of Seiberg-like dualities (level-rank duality between gauged Wess–Zumino–Witten theories. The arguments in use to identify a potential dual for the supersymmetric WZW theory based on the coset U(N+MkU(Nk can be extended to be applied to a wider variety of gauge groups, notably USp(2N+2M2kUSp(2N2k and SO(2N+2M2kSO(2N2k, which will be dealt with briefly. Most interestingly, non-supersymmetric versions of the latter theories can also be shown to have duals in a similar fashion. These results are supported by several pieces of evidence, string phenomenological interpretations of Seiberg duality, even in non-supersymmetric backgrounds, are helpful to justify the formulation, then, from field theory, quantities such as central charges or Witten indices are shown to match exactly. The stability of these non-supersymmetric models is also discussed and shown to be consistent.
Supersymmetric axion grand unified theories and their predictions
Co, Raymond T.; D'Eramo, Francesco; Hall, Lawrence J.
2016-10-01
We introduce a class of unified supersymmetric axion theories with unified and Peccei-Quinn (PQ) symmetries broken by the same set of fields at a scale ˜2 ×1 016 GeV . A typical domain wall number of order 30 leads to an axion decay constant fa of order 1 015 GeV . Inflation generates a large saxion condensate, giving a reheat temperature TR below the QCD scale for supersymmetry breaking of order 1-10 TeV. Axion field oscillations commence in the saxion matter-dominated era near the QCD scale, and recent lattice computations of the temperature dependence of the axion mass in this era allow a controlled calculation of the axion dark matter abundance. The observed abundance can be successfully explained by an initial axion misalignment angle of order unity, θi˜1 . A highly correlated set of predictions is discussed for fa, TR, the supersymmetric Higgs mass parameter μ , the amount of dark radiation Δ Neff, the proton decay rate Γ (p →e+π0), isocurvature density perturbations and the B mode of the cosmic microwave background. The last two are particularly interesting when the energy scale of inflation is also of order 1 016 GeV .
Confining strings in supersymmetric theories with Higgs branches
Shifman, M.; Tallarita, Gianni; Yung, Alexei
2015-03-01
We study flux tubes (strings) on the Higgs branches in supersymmetric gauge theories. In generic vacua on the Higgs branches, strings were shown to develop long-range "tails" associated with massless fields, a characteristic feature of the Higgs branch (the only exception is the vacuum at the base of the Higgs branch). A natural infrared regularization for the above tails is provided by a finite string length L . We perform a numerical study of these strings in generic vacua. We focus on the simplest example of strings in N =1 supersymmetric QED with the Fayet-Iliopoulos term. In particular, we examine the accuracy of a logarithmic approximation (proposed earlier by Evlampiev and Yung) for the tension of such string solutions. In the Evlampiev-Yung formula, the dependence of tension on the string length is logarithmic, and the dependence on the geodesic length from the base of the Higgs branch is quadratic. We observe a remarkable agreement of our numerical results for the string tension with the Evlampiev-Yung analytic expression.
Confining Strings in Supersymmetric Theories with Higgs Branches
Shifman, Mikhail; Yung, Alexei
2014-01-01
We study flux tubes (strings) on the Higgs branches in supersymmetric gauge theories. In generic vacua on the Higgs branches strings were shown to develop long-range "tails" associated with massless fields, a characteristic feature of the Higgs branch (the only exception is the vacuum at the base of the Higgs branch). A natural infrared regularization for the above tails is provided by a finite string length L. We perform a numerical study of these strings in generic vacua. We focus on the simplest example of strings in N=1 supersymmetric QED with the Fayet-Iliopoulos term. In particular, we examine the accuracy of a logarithmic approximation (proposed earlier by Evlampiev and Yung) for the tension of such string solutions. In the Evlampiev-Yung formula the dependence of tension on the string length is logarithmic and the dependence on the geodesic length from the base of the Higgs branch is quadratic. We observe a remarkable agreement of our numerical results for the string tension with the Evlampiev-Yung an...
Functional renormalisation group equations for supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Synatschke-Czerwonka, Franziska
2011-01-11
This work is organised as follows: In chapter 2 the basic facts of quantum field theory are collected and the functional renormalisation group equations are derived. Chapter 3 gives a short introduction to the main concepts of supersymmetry that are used in the subsequent chapters. In chapter 4 the functional RG is employed for a study of supersymmetric quantum mechanics, a supersymmetric model which are studied intensively in the literature. A lot of results have previously been obtained with different methods and we compare these to the ones from the FRG. We investigate the N=1 Wess-Zumino model in two dimensions in chapter 5. This model shows spontaneous supersymmetry breaking and an interesting fixed-point structure. Chapter 6 deals with the three dimensional N=1 Wess-Zumino model. Here we discuss the zero temperature case as well as the behaviour at finite temperature. Moreover, this model shows spontaneous supersymmetry breaking, too. In chapter 7 the two-dimensional N=(2,2) Wess-Zumino model is investigated. For the superpotential a non-renormalisation theorem holds and thus guarantees that the model is finite. This allows for a direct comparison with results from lattice simulations. (orig.)
Theory and Phenomenology of an Exceptional Supersymmetric Standard Model
King, S F; Nevzorov, R
2006-01-01
We make a comprehensive study of the theory and phenomenology of a low energy supersymmetric standard model originating from a string-inspired $E_6$ grand unified gauge group. The Exceptional Supersymmetric Standard Model (ESSM) considered here is based on the low energy SM gauge group together with an extra $Z'$ corresponding to an extra $U(1)_{N}$ gauge symmetry under which right--handed neutrinos have zero charge. The low energy matter content of the ESSM corresponds to three 27 representations of the $E_6$ symmetry group, to ensure anomaly cancellation, plus an additional pair of Higgs--like doublets as required for high energy gauge coupling unification. The ESSM is therefore a low energy alternative to the MSSM or NMSSM. The ESSM involves extra matter beyond the MSSM contained in three $5+5^*$ representations of SU(5), plus three SU(5) singlets which carry $U(1)_{N}$ charges, one of which develops a VEV, providing the effective $\\mu$ term for the Higgs doublets, as well as the necessary exotic fermion m...
Supersymmetric M5 Brane Theories on R x CP2
Kim, Hee-Cheol
2012-01-01
We propose 4 and 12 supersymmetric Yang-Mills-Chern-Simons theories on $\\mathrm{R\\times CP^2}$ obtained by twisted $\\mathrm{Z}_k$ moddings and dimensional reduction of the 6d (2,0) superconformal field theories on $\\mathrm{R\\times S^5}$. These theories have a discrete coupling constant $\\frac{1}{g^2_{YM}} =\\frac{k}{4\\pi^2}$ so that instantons represent the Kaluza-Klein modes correctly. We calculate the perturbative part of the SU(N) gauge group Euclidean path integral for the index function and confirm it with the known half-BPS index. The scalar and fermionic fields have the conformal dimension prescribed by the 6d theory. From the similar twisted $Z_k$ modding of the $\\mathrm{AdS_7\\times S^4}$ geometry, we speculate that the $M$ region is for $k\\lesssim N^{1/3}$ and the type IIA region is $N^{1/3}\\lesssim k \\lesssim N$. When nonperturbative corrections are included, our theory is expected to produce the full index of the 6d (2,0) theory.
Domain Walls in Supersymmetric Yang-Mills Theories
Kaplunovsky, V S; Yankielowicz, Shimon; Kaplunovsky, Vadim S.; Sonnenschein, Jacob; Yankielowicz, Shimon
1999-01-01
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of the domain wall. The wall has a sandwich-like five-layer structure of three distinct phases -- electric confinement, Coulomb and oblique confinement -- separated by two separate transition regions. For larger scalar masses, the three-phase structure disappears and the Seiberg-Witten theory becomes inadequate because of two major problems: First, the higher-derivative interactions between the light fields become relevant and second, both the magnetic monopole condensate and the dyon condensate show up in the same region of space, a phenomenon indescribable in terms of a local field theory. Nevertheless, we argue that the BPS saturated domain wall continues to exist in this regime and give a qualitative description of the scalar and gaugino condensates. Finally, we discuss ...
Non-perturbative Solutions to N=2 Supersymmetric Yang-Mills Theories Progress and Perspective
Ohta, Y
1999-01-01
This note reviews the progress on the low energy dynamics of N=2 supersymmetric Yang-Mills theories after the works of Seiberg and Witten. Specifically, the theory of prepotential for non-specialists is reviewed.
Eto, Minoru
2014-01-01
Dyonic non-Abelian local/semi-global vortex strings are studied in detail in supersymmetric/non-supersymmetric Yang-Mills-Higgs theories. While the BPS tension formula is known to be the same as that for the BPS dyonic instanton, we find that the non-BPS tension formula is approximated very well by the well-known tension formula of the BPS dyon. We show that this mysterious tension formula for the dyonic non-BPS vortex stings can be understood from the perspective of a low energy effective field theory. Furthermore, we propose an efficient method to obtain an effective theory of a single vortex string, which includes not only lower derivative terms but also all order derivative corrections by making use of the tension formula. We also find a novel dyonic vortex string whose internal orientation vectors rotate in time and spiral along the string axis.
On supersymmetric Chern-Simons-type theories in five dimensions
Kuzenko, Sergei M
2014-01-01
We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor multiplet is described in superspace for the first time.
Low-energy effective action in N = 2 supersymmetric field theories
Bukhbinder, E I; Bukhbinder, I L; Ivanov, E A; Kuzenko, S M
2001-01-01
Review of new approach to finding effective action in N = 2 and N = 4 supersymmetric theory is given. The approach is based on the formulation of these theories in terms of unconstrained superfields in harmonic superspace. Construction of superfield model of N = 2 supersymmetric field theory (hypermultiplet, N = 2 supersymmetric Yang-Mills theory) is discussed. N = 2 background field method is considered. Perturbative holomorphic effective potential in N = 2 models and non-holomorphic effective potential in N = 4 Yang-Mills field theory, defining exact low-energy effective action in this theory, are studied. Possible applications of low-energy effective action in supersymmetric theories and some open problems are discussed. Comparison of given approach with others is performed
Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum
Nozari, Kourosh; Balef, F Rezaee
2013-01-01
We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra $[x,p]=i\\hbar\\big(1-\\beta p+2\\beta^{2}p^{2}\\big)$, where $\\beta $ is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.
On the Supersymmetric Index of the M-theory 5-brane and Little String Theory
Bonelli, G
2001-01-01
We propose a six-dimensional framework to calculate the supersymmetric index of M-theory 5-branes wrapped on a six-manifold with product topology $M_4\\times T^2$, where $M_4$ is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is obtained by zero-modes counting of the self-dual tensor contribution plus ``little'' string states and correctly reproduces the known results which can be obtained by shrinking or blowing the $T^2$ volume parameter. We also extract the geometric moduli space of the multi M5-brane system and infer the generic structure of the supersymmetric index for more general geometries.
Fluxes, hierarchies, and metastable vacua in supersymmetric field theories
Energy Technology Data Exchange (ETDEWEB)
Bruemmer, F.
2008-02-06
This thesis concerns topics both in low-energy effective field theories from type IIB superstring flux compactifications and in four-dimensional, rigidly supersymmetric gauge theories. We introduce flux compactifications with so-called ''warped throat'' regions, which lead to large hierarchies of scales in the effective four-dimensional theory. The correspondence between a particular such throat and a five-dimensional Randall-Sundrum-like model is established. We shown how certain string-theoretic features of the compactification, such as moduli stabilization by fluxes or the presence of an unstabilized Kaehler modulus, are incorporated in the five-dimensional picture. The KKLT construction for metastable de Sitter vacua is reviewed, as well as some possible modifications involving spontaneous F-term supersymmetry breaking. For KKLT-like models with their hidden sector localized inside a throat, the mediation of supersymmetry breaking to the visible sector is investigated. We review the mechanism of mixed modulus-anomaly mediation, and show that there can be additional equally important gravity-mediated contributions. We finally turn to the ISS model of metastable dynamical supersymmetry breaking in four dimensions, and present a renormalizable extension which generates a large hierarchy naturally. We also recapitulate how the ISS model may be obtained from a type IIB superstring model. (orig.)
Phase diagrams of exceptional and supersymmetric lattice gauge theories
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Wellegehausen, Bjoern-Hendrik
2012-07-10
In this work different strongly-coupled gauge theories with and without fundamental matter have been studied on the lattice with an emphasis on the confinement problem and the QCD phase diagram at nonvanishing net baryon density as well as on possible supersymmetric extensions of the standard model of particle physics. In gauge theories with a non-trivial centre symmetry, as for instance SU(3)-Yang-Mills theory, confinement is intimately related to the centre of the gauge group, and the Polyakov loop serves as an order parameter for confinement. In QCD, this centre symmetry is explicitly broken by quarks in the fundamental representation of the gauge group. But still quarks and gluons are confined in mesons, baryons and glueballs at low temperatures and small densities, suggesting that centre symmetry is not responsible for the phenomenon of confinement. Therefore it is interesting to study pure gauge theories without centre symmetry. In this work this has been done by replacing the gauge group SU(3) of the strong interaction with the exceptional Lie group G{sub 2}, that has a trivial centre. To investigate G{sub 2} gauge theory on the lattice, a new and highly efficient update algorithm has been developed, based on a local HMC algorithm. Employing this algorithm, the proposed and already investigated first order phase transition from a confined to a deconfined phase has been confirmed, showing that indeed a first order phase transition without symmetry breaking or an order parameter is possible. In this context, also the deconfinement phase transition of the exceptional Lie groups F4 and E6 in three spacetime dimensions has been studied. It has been shown that both theories also possess a first order phase transition.
On supermatrix models, Poisson geometry, and noncommutative supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Klimčík, Ctirad [Aix Marseille Université, CNRS, Centrale Marseille I2M, UMR 7373, 13453 Marseille (France)
2015-12-15
We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.
Cosmological implications of a supersymmetric extension of the Brans-Dicke theory
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Catena, R.
2007-09-15
In the Brans-Dicke theory the Planck mass is replaced by a dynamical scalar field. We consider here the supersymmetric analogous of this mechanism replacing in the supergravity Lagrangian the Planck mass with a chiral superfield. This analysis is motivated by the research of possible connections between supersymmetric Dark Matter scenarios and Dark Energy models based on Brans-Dicke-like theories. We find that, contrary to the original Brans-Dicke theory, in its supersymmetric analogous the gravitational sector does not couple to the matter sector in a universal metric way. As a result, violations of the weak equivalence principle could be present in such a scenario. (orig.)
New Non-Trivial Vacuum Structures in Supersymmetric Field Theories
Dienes, Keith R
2009-01-01
In this talk, we present three examples of new non-trivial vacuum structures that can occur in supersymmetric field theories, along with explicit models in which they arise. The first vacuum structure is one in which supersymmetry is broken at tree-level in a perturbative theory that also contains a supersymmetry-preserving ground state. Models realizing this structure are uniquely characterized by the fact that no flat directions appear in the classical potential, all vacua appear at finite distances in field space, and no non-perturbative physics is required for vacuum stability. The second non-trivial vacuum structure we discuss consists of large (and even infinite) towers of metastable vacua, and we show that models which give rise to such vacuum towers exhibit a rich set of instanton-induced vacuum tunneling dynamics. Finally, our third new non-trivial vacuum structure consists of an infinite number of degenerate vacua; this leads to a Bloch-wave ground state and a vacuum "band" structure. Models with su...
Formulation of Free Higher Spin Supersymmetric Theories in Superspace
Phillips, J
2005-01-01
The N = 1 superfield formalism in four-dimensions is well formulated and understood, yet there remain unsolved problems. In this thesis, superfield actions for free massless and massive higher spin superfield theories are formulated in four dimensions. The discussion of massless models is restricted to half integer superhelicity. These models describe multiplets with helicities (s, s-1/2) where s is an integer. The investigation of massive models covers recent work on superspin-3/2 and superspin-1 multiplets. Superspin-3/2 multiplets contain component fields with spins (2, 3/2, 3/2, 1) and superspin-1 multiplets contain component fields with spins (3/2, 1, 1, 1/2). The super projector method is used to distinguish supersymmetric subspaces. Here, this method is used to write general superspace actions. The underlying geometrical structure of superspace actions is elucidated when they are written in terms of super projectors. This thesis also discusses the connection between four-dimensional massive theories an...
Supersymmetric gauge theories on the lattice: Pfaffian phases and the Neuberger 0/0 problem
Mehta, Dhagash; Galvez, Richard; Joseph, Anosh
2011-01-01
Recently a class of supersymmetric gauge theories have been successfully implemented on the lattice. However, there has been an ongoing debate on whether lattice versions of some of these theories suffer from a sign problem, with independent simulations for the ${\\cal N} = (2, 2)$ supersymmetric Yang-Mills theories in two dimensions yielding seemingly contradictory results. Here, we address this issue from an interesting theoretical point of view. We conjecture that the sign problem observed in some of the simulations is related to the so called Neuberger 0/0 problem, which arises in ordinary non-supersymmetric lattice gauge theories, and prevents the realization of Becchi-Rouet-Stora-Tyutin symmetry on the lattice. After discussing why we expect a sign problem in certain classes of supersymmetric lattice gauge theories far from the continuum limit, we argue that these problems can be evaded by use of a non-compact parametrization of the gauge link fields.
Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-11
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Gama, F S; Nascimento, J R; Petrov, A Yu; da Silva, A J
2015-01-01
We explicitly calculate the one-loop effective potential for the supersymmetric topologically massive gauge theory in four dimensions, where the chiral scalar superfield is directly coupled to the field strength for the gauge spinor superfield.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
Assel, Benjamin; Murthy, Sameer; Yokoyama, Daisuke
2016-01-01
We study supersymmetric gauge theories with an R-symmetry, defined on non-compact, hyperbolic, Riemannian three-manifolds, focusing on the case of a supersymmetry-preserving quotient of Euclidean AdS$_3$. We compute the exact partition function in these theories, using the method of localization, thus reducing the problem to the computation of one-loop determinants around a supersymmetric locus. We evaluate the one-loop determinants employing three different techniques: an index theorem, the method of pairing of eigenvalues, and the heat kernel method. Along the way, we discuss aspects of supersymmetry in manifolds with a conformal boundary, including supersymmetric actions and boundary conditions.
Effects of heavy modes on vacuum stability in supersymmetric theories
Brizi, Leonardo
2010-01-01
We study the effects induced by heavy fields on the masses of light fields in supersymmetric theories, under the assumption that the heavy mass scale is much higher than the supersymmetry breaking scale. We show that the square-masses of light scalar fields can get two different types of significant corrections when a heavy multiplet is integrated out. The first is an indirect level-repulsion effect, which may arise from heavy chiral multiplets and is always negative. The second is a direct coupling contribution, which may arise from heavy vector multiplets and can have any sign. We then apply these results to the sGoldstino mass and study the implications for the vacuum metastability condition. We find that the correction from heavy chiral multiplets is always negative and tends to compromise vacuum metastability, whereas the contribution from heavy vector multiplets is always positive and tends on the contrary to reinforce it. These two effects are controlled respectively by Yukawa couplings and gauge charg...
BPS Boojums in N=2 supersymmetric gauge theories II
Arai, Masato; Eto, Minoru
2016-01-01
We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in N=2 supersymmetric Abelian gauge theories in four dimensions. In this work, we numerically confirm that a boojum appearing at an end point of a string on a thick domain wall behaves as a magnetic monopole with a fractional charge in three dimensions. We introduce a "magnetic" scalar potential whose gradient gives magnetic fields. Height of the magnetic potential has a geometrical meaning that is shape of the domain wall. We find a semi-local extension of boojum which has an additional size moduli at an end point of a semi-local string on the domain wall. Dyonic solutions are also studied and we numerically confirm that the dyonic domain wall becomes an electric capacitor storing opposite electric charges on its skins. At the same time, the boojum becomes fractional dyon whose charge density is proportional to ${\\vec E} \\cdot {\\vec B}$. We also study dual configurations with an in...
BPS Boojums in N=2 supersymmetric gauge theories
Arai, Masato; Eto, Minoru
2016-01-01
We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in N=2 supersymmetric Abelian gauge theories in four dimensions. We obtain solutions to the 1/4 BPS equations with the finite gauge coupling constant. To obtain numerical solutions for generic coupling constants, we construct globally correct approximate functions which allow us to easily find fixed points of a gradient flow equations. We analytically/numerically confirm that the negative mass of a single boojum appearing at the end point of the vortex string on the logarithmically bent domain wall is equal to the half-mass of the 't Hooft-Polyakov monopole. We examine various configurations and clarify how the shape of the boojum depends on the coupling constants and moduli parameters. We find a semi-local boojum with a size moduli which appears when the semi-local string ends on the domain wall. We introduce a magnetic scalar potential which offers an intuitive understanding that the end point of...
Energy Technology Data Exchange (ETDEWEB)
Manousselis, Pantelis [Department of Engineering Sciences, University of Patras, 26110 Patras (Greece) and Physics Department, National Technical University, Zografou Campus, 15780 Athens (Greece)]. E-mail: pman@central.ntua.gr; Zoupanos, George [Department of Engineering Sciences, University of Patras, 26110 Patras (Greece); Physics Department, National Technical University, Zografou Campus, 15780 Athens (Greece)
2004-11-01
A ten-dimensional supersymmetric gauge theory is written in terms of N=1, D=4 superfields. The theory is dimensionally reduced over six-dimensional coset spaces. We find that the resulting four-dimensional theory is either a softly broken N = 1 supersymmetric gauge theory or a non-supersymmetric gauge theory depending on whether the coset spaces used in the reduction are non-symmetric or symmetric. In both cases examples susceptible to yield realistic models are presented. (author)
Energy Technology Data Exchange (ETDEWEB)
Bossard, G
2007-10-15
This thesis contains 2 parts based on scientific contributions that have led to 2 series of publications. The first one concerns the introduction of vector symmetry in cohomological theories, through a generalization of the so-called Baulieu-Singer equation. Together with the topological BRST (Becchi-Rouet-Stora-Tyutin) operator, this symmetry gives an off-shell closed sub-sector of supersymmetry that permits to determine the action uniquely. The second part proposes a methodology for re-normalizing supersymmetric Yang-Mills theory without assuming a regularization scheme which is both supersymmetry and gauge invariance preserving. The renormalization prescription is derived thanks to the definition of 2 consistent Slavnov-Taylor operators for supersymmetry and gauge invariance, whose construction requires the introduction of the so-called shadow fields. We demonstrate the renormalizability of supersymmetric Yang-Mills theories. We give a fully consistent, regularization scheme independent, proof of the vanishing of the {beta} function and of the anomalous dimensions of the one half BPS operators in maximally supersymmetric Yang-Mills theory. After a short introduction, in chapter two, we give a review of the cohomological Yang-Mills theory in eight dimensions. We then study its dimensional reductions in seven and six dimensions. The last chapter gives quite independent results, about a geometrical interpretation of the shadow fields, an unpublished work about topological gravity in four dimensions, an extension of the shadow formalism to superconformal invariance, and finally the solution of the constraints in a twisted superspace. (author)
Some Aspects of Supersymmetric Field Theories with Minimal Length and Maximal Momentum
Directory of Open Access Journals (Sweden)
Kourosh Nozari
2013-01-01
Full Text Available We consider a real scalar field and a Majorana fermion field to construct a supersymmetric quantum theory of free fermion fields based on the deformed Heisenberg algebra [ x , p ] = i ℏ ( 1 − β p + 2 β 2 p 2 , where β is a deformation parameter. We present a deformed supersymmetric algebra in the presence of minimal length and maximal momentum.
Calabi-Yau compactifications of non-supersymmetric heterotic string theory
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Blaszczyk, Michael [Mainz Univ. (Germany). PRISMA Cluster of Excellence and Inst. fuer Physik (WA THEP); Groot Nibbelink, Stefan [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; Loukas, Orestis [Muenchen Univ. (Germany). Arnold Sommerfeld Center for Theoretical Physics; National Technical Univ. Athens (Greece). School of Electrical and Computer Engineering; Ruehle, Fabian [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
2015-07-15
Phenomenological explorations of heterotic strings have conventionally focused primarily on the E{sub 8} x E{sub 8} theory. We consider smooth compactifications of all three ten-dimensional heterotic theories to exhibit the many similarities between the non-supersymmetric SO(16) x SO(16) theory and the related supersymmetric E{sub 8} x E{sub 8} and SO(32) theories. In particular, we exploit these similarities to determine the bosonic and fermionic spectra of Calabi-Yau compactifications with line bundles of the nonsupersymmetric string. We use elements of four-dimensional supersymmetric effective field theory to characterize the non-supersymmetric action at leading order and determine the Green-Schwarz induced axion-couplings. Using these methods we construct a non-supersymmetric Standard Model(SM)-like theory. In addition, we show that it is possible to obtain SM-like models from the standard embedding using at least an order four Wilson line. Finally, we make a proposal of the states that live on five branes in the SO(16) x SO(16) theory and find under certain assumptions the surprising result that anomaly factorization only admits at most a single brane solution.
Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
Lee, Bum-Hoon; Yang, Hyun Seok
2016-01-01
We study localization of five-dimensional supersymmetric $U(1)$ gauge theory on $\\mathbb{S}^3 \\times \\mathbb{R}_{\\theta}^{2}$ where $\\mathbb{R}_{\\theta}^{2}$ is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric $U(N \\to \\infty)$ gauge theory on $\\mathbb{S}^3$ using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space $\\mathbb{R}_{\\theta}^{2}$ allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC $U(1)$ gauge theory. The result shows a rich duality between NC $U(1)$ gauge theories and large $N$ matrix models in various dimensions.
5-brane webs, symmetry enhancement, and duality in 5d supersymmetric gauge theory
Energy Technology Data Exchange (ETDEWEB)
Bergman, Oren [Department of Physics, Technion, Israel Institute of Technology,Haifa, 32000 (Israel); Rodríguez-Gómez, Diego [Department of Physics, Universidad de Oviedo,Avda. Calvo Sotelo 18, 33007, Oviedo (Spain); Zafrir, Gabi [Department of Physics, Technion, Israel Institute of Technology,Haifa, 32000 (Israel)
2014-03-25
We present a number of investigations of 5d N=1 supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed point theory corresponding to SU(N) gauge theory with Chern-Simons level ±N, enhanced global symmetries in quiver theories, and dualities between quiver theories and non-quiver theories. Instanton contributions play a crucial role throughout.
Nibbelink, Stefan Groot
2016-01-01
Inspired by the tachyon-free non-supersymmetric heterotic SO(16)xSO(16) string we consider a special class of non-supersymmetric field theories: Those that can be obtained from supersymmetric field theories by supersymmetry breaking twists. We argue that such theories, like their supersymmetric counter parts, may still possess some fermionic symmetries as left-overs of the super gauge transformations and have special one-loop non-renormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking corrections.
On geometric aspects of the supersymmetric Fokas-Gel’fand immersion formula
Bertrand, S.
2017-09-01
In this paper, we develop a new geometric characterization for the supersymmetric versions of the Fokas-Gel’fand formula for the immersion of soliton supermanifolds with two bosonic and two fermionic independent variables into Lie superalgebras. In order to do so, from a linear spectral problem of a supersymmetric integrable system using the covariant fermionic derivative, we provide a technique to obtain two additional linear spectral problems for that integrable system, one using the bosonic variable derivatives and the other using the fermionic variable derivatives. This allows us to investigate, through the first and second fundamental forms, the geometry of the (1+1\\vert2 )-supermanifolds immersed in Lie superalgebras. Whenever possible, the mean and Gaussian curvatures of the supermanifolds are calculated. These theoretical considerations are applied to the supersymmetric sine-Gordon equation.
Supersymmetric gauged Double Field Theory: Systematic derivation by virtue of \\textit{Twist}
Cho, Wonyoung; Jeon, Imtak; Park, Jeong-Hyuck
2015-01-01
In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete covariantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the $D=10$ untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the $32$ supersymmetries unbroken.
Non-Supersymmetric CS-Matter Theories with Known AdS Duals
Directory of Open Access Journals (Sweden)
Davide Forcella
2011-01-01
Full Text Available We consider three-dimensional conformal field theories living on a stack of N anti-M2 branes at the tip of eight-dimensional supersymmetric cones. The corresponding supergravity solution is obtained by changing sign to the four-form in the Freund-Rubin solution representing M2 branes (“skew-whiffing” transformation and it is known to be stable. The existence of these non-supersymmetric, stable field theories, at least in the large N limit, is a peculiarity of the AdS 4 / CFT 3 correspondence with respect to the usual AdS 5 / CFT 4 , and it is worthwhile to study it. We analyze in detail the KK spectrum of the skew-whiffed solution associated with S 7 / ℤ k and we speculate on the natural field content for a candidate non-supersymmetric dual field theory.
Non-supersymmetric CS-matter theories with known AdS duals
Forcella, Davide
2011-01-01
We consider three dimensional conformal field theories living on a stack of N anti-M2 branes at the tip of eight-dimensional supersymmetric cones. The corresponding supergravity solution is obtained by changing sign to the four-form in the Freund-Rubin solution representing M2 branes ("skew-whiffing" transformation) and it is known to be stable. The existence of these non supersymmetric, stable field theories, at least in the large N limit, is a peculiarity of the AdS4/CFT3 correspondence with respect to the usual AdS5/CFT4, and it is worthwhile to study it. We analyze in detail the KK spectrum of the skew-whiffed solution associated with S^7/Z_k and we speculate on the natural field content for a candidate non-supersymmetric dual field theory.
Simple perturbative renormalization scheme for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Foda, O.E. (Purdue Univ., Lafayette, IN (USA). Dept. of Physics)
1983-06-30
We show that the manifestly supersymmetric and gauge-invariant results of Supersymmetric Dimensional renormalization (SDR) are reproduceable through a simple, and mathematically consistent perturbative renormalization technique, where regularization is attained via a map that deforms the momentum space Feynman integrands in a specific way. In particular, it introduces a multiplicative factor of ((p+q)/..delta..)/sup -/delta in each momentum-space loop integral, where p is the magnitude of the loop momentum, q is an arbitrary constant to be chosen as will be explained, thus compensating for loss of translation invariance in p, ..lambda.. is a renormalization mass, and delta is a suitable non-integer: the analog of epsilon in dimensional schemes. All Dirac algebra and integration are four-dimensional, and renormalization is achieved by subtracting poles in delta, followed by setting delta->O. The mathematical inconsistencies of SDR are evaded by construction, since the numbers of fermion and boson degrees of freedom remain unchanged but analytic continuation in the number of dimensions is bypassed. Thus, the technique is equally viable in component and in superfield formalisms, and all anomalies are realized. The origin of the chiral anomaly is that no choice of q satisfies both gauge and chiral Ward identities simultaneously.
Implications of a heavy top in supersymmetric theories
Leontaris, George K
1995-01-01
In the context of the radiative electroweak symmetry breaking scenario we investigate the implications of a heavy top quark mass, close to its infrared fixed point, on the low energy parameters of the minimal supersymmetric standard model. We use analytic expressions to calculate the Higgs masses as well as the supersymmetric masses of the third generation. We further assume bottom-tau unification at the GUT scale and examine the constraints put by this condition on the parameter space (\\tan\\beta,\\alpha_3), using the renormalization group procedure at the two-loop level. We find only a small fraction of the parameter space where the above conditions can be satisfied, namely 1\\le \\tan\\beta \\le 2, while 0.111\\le\\alpha_3(M_Z) \\le 0.118. We further analyse the case where all three Yukawa couplings reach the perturbative limit just after the unification scale. In this latter case, the situation turns out to be very strict demanding \\tan\\beta\\sim 63.
Transport properties of N=4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, P; Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled N=4 supersymmetric SU(n) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n N=4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation for the shear and the sound wave lowest quasinormal modes in the leading order alpha'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the alpha'-corrected nonextremal black branes in string theory.
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
The low-lying spectrum of N=1 supersymmetric Yang-Mills theory
Bergner, Georg; Montvay, Istvan; Muenster, Gernot; Piemonte, Stefano
2015-01-01
The spectrum of the lightest bound states in N=1 supersymmetric Yang-Mills theory with SU(2) gauge group, calculated on the lattice, is presented. The masses have first been extrapolated towards vanishing gluino mass and then to the continuum limit. The final picture is consistent with the formation of degenerate supermultiplets.
Localization of 3d $\\mathcal{N}=2$ Supersymmetric Theories on $S^1 \\times D^2$
Yoshida, Yutaka
2014-01-01
We study three dimensional N=2 supersymmetric Chern-Simons-Matter theories on the direct product of circle and two dimensional hemisphere (S^1 x D^2) with specified boundary conditions by the method of localization. We construct boundary interactions to cancel the supersymmetric variation of three dimensional superpotential term and Chern-Simons term and show inflows of bulk-boundary anomalies. It finds that the boundary conditions induce two dimensional N=(0,2) type supersymmetry on the boundary torus. We also study the relation between the 3d-2d coupled partition function of our model and three dimensional holomorphic blocks.
On the Stability of Non-Supersymmetric Quantum Attractors in String Theory
Dominic, Pramod
2011-01-01
We study four dimensional non-supersymmetric attractors in type IIA string theory in the presence of sub-leading corrections to the prepotential. For a given Calabi-Yau manifold, the D0-D4 system admits an attractor point in the moduli space which is uniquely specified by the black hole charges. The perturbative corrections to the prepotential do not change the number of massless directions in the black hole effective potential. We further study non-supersymmetric D0-D6 black holes in the presence of sub-leading corrections. In this case the space of attractor points define a hypersurface in the moduli space.
Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule
Kato, Mitsuhiro; So, Hiroto
2016-01-01
N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.
All-loop Analysis of UV Divergences in Maximally Supersymmetric Gauge Theories
Borlakov, A T; Tolkachev, D M; Vlasenko, D E
2016-01-01
We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results.
A supersymmetric theory of vector-like leptons
Joglekar, Aniket; Schwaller, Pedro; Wagner, Carlos E. M.
2013-07-01
We study a supersymmetric extension of the vector-like lepton scenario, such that the vacuum instability induced by large lepton Yukawa couplings is lifted by the presence of superpartners at or below the TeV scale. In order to preserve the unification of gauge couplings, we introduce a full 16+overline{16} of SO(10), and determine the maximal possible values for the Yukawa couplings consistent with perturbativity at the GUT scale. We find that the Higgs to diphoton decay rate can be enhanced by up to 50% while maintaining vacuum stability and keeping the new particle masses above 100 GeV, while larger enhancements are possible if the masses of the new particles are lowered further.
A Supersymmetric Theory of Vector-like Leptons
Joglekar, Aniket; Wagner, Carlos E M
2013-01-01
We study a supersymmetric extension of the vector-like lepton scenario, such that the vacuum instability induced by large lepton Yukawa couplings is lifted by the presence of superpartners at or below the TeV scale. In order to preserve the unification of gauge couplings, we introduce a full 16+\\bar{16} of SO(10), and determine the maximal possible values for the Yukawa couplings consistent with perturbativity at the GUT scale. We find that the Higgs to diphoton decay rate can be enhanced by up to 50% while maintaining vacuum stability and keeping the new particle masses above 100 GeV, while larger enhancements are possible if the masses of the new particles are lowered further.
Matsuura, So; Ohta, Kazutoshi
2014-01-01
We define supersymmetric Yang-Mills theory on an arbitrary two-dimensional lattice (polygon decomposition) with preserving one supercharge. When a smooth Riemann surface $\\Sigma_g$ with genus $g$ emerges as an appropriate continuum limit of the generic lattice, the discretized theory becomes topologically twisted $\\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory on $\\Sigma_g$. If we adopt the usual square lattice as a special case of the discretization, our formulation is identical with Sugino's lattice model. Although the tuning of parameters is generally required while taking the continuum limit, the number of the necessary parameters is at most two because of the gauge symmetry and the supersymmetry. In particular, we do not need any fine-tuning if we arrange the theory so as to possess an extra global $U(1)$ symmetry ($U(1)_{R}$ symmetry) which rotates the scalar fields.
Dorey, N; Mattis, M P; Slater, M J; Weir, W A
1997-01-01
We discuss the contribution of ADHM multi-instantons to the higher-derivative terms in the gradient expansion along the Coulomb branch of N=2 and N=4 supersymmetric SU(2) gauge theories. In particular, using simple scaling arguments, we confirm the Dine-Seiberg nonperturbative nonrenormalization theorems for the 4-derivative/8-fermion term in the two finite theories (N=4, and N=2 with N_F=4).
$\\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
Aprile, Francesco
2016-01-01
General half-BPS A-type boundary conditions are formulated for N=2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.
Exact results for vortex loop operators in 3d supersymmetric theories
Drukker, Nadav; Okuda, Takuya; Passerini, Filippo
2014-07-01
Three dimensional field theories admit disorder line operators, dubbed vortex loop operators. They are defined by the path integral in the presence of prescribed singularities along the defect line. We study half-BPS vortex loop operators for = 2 supersymmetric theories on 3, its deformation and 1 × 2. We construct BPS vortex loops defined by the path integral with a fixed gauge or flavor holonomy for infinitesimal curves linking the loop. It is also possible to include a singular profile for matter fields. For vortex loops defined by holonomy, we perform supersymmetric localization by calculating the fluctuation modes, or alternatively by applying the index theory for transversally elliptic operators. We clarify how the latter method works in situations without fixed points of relevant isometries. Abelian mirror symmetry transforms Wilson and vortex loops in a specific way. In particular an ordinary Wilson loop transforms into a vortex loop for a flavor symmetry. Our localization results confirm the predictions of abelian mirror symmetry.
The gravity dual of supersymmetric gauge theories on a squashed three-sphere
Energy Technology Data Exchange (ETDEWEB)
Martelli, Dario [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Passias, Achilleas, E-mail: achilleas.passias@kcl.ac.uk [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)
2012-11-21
We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a U(1) Multiplication-Sign U(1)-invariant squashed three-sphere, with a non-trivial background gauge field. This is described by a supersymmetric solution of four-dimensional N=2 gauged supergravity with a non-trivial instanton for the graviphoton field. The particular gauge theory in turn determines the lift to a solution of eleven-dimensional supergravity. We compute the partition function for a class of Chern-Simons quiver gauge theories on both sides of the duality, in the large N limit, finding precise agreement for the functional dependence on the squashing parameter. This constitutes an exact check of the gauge/gravity correspondence in a non-conformally invariant setting.
Institute of Scientific and Technical Information of China (English)
李季根; 颜骏; 邹伯夏; 苏文杰
2011-01-01
A sine-Gordon soliton star model with the action of exotic matter and dark energy is studied in this article, the solutions of state equation and mass of star are calculated by using field equation. We found that the density and pressure of matter are connected with the soliton state and the mass of star. Moreover, star equilibrium and stability of dark energy are analyzed and discussed, the result shown that the state of soliton star interior exist in the form of mixed state.%研究了具有奇异物质和暗能量作用的sine-Gordon孤子星模型,根据场方程计算了物态方程的解和星体质量,发现物质密度和压强与孤子态和星体质量有关.另外,还对星体平衡和暗能量的稳定性质进行了分析和讨论,结果表明孤子星内部以奇异物质与暗能量的混合态形式存在.
The a-function for N=2 supersymmetric gauge theories in three dimensions
Gracey, J A; Poole, C; Schroder, Y
2016-01-01
Recently, the existence of a candidate a-function for renormalisable theories in three dimensions was demonstrated for a general theory at leading order and for a scalar-fermion theory at next-to-leading order. Here we extend this work by constructing the a-function at next-to-leading order for an N=2 supersymmetric Chern-Simons theory. This increase in precision for the a-function necessitated the evaluation of the underlying renormalization-group functions at four loops.
The gravity dual of supersymmetric gauge theories on a squashed $S^1 \\times S^3$
Cassani, Davide
2014-01-01
We present a new one-parameter family of supersymmetric solutions deforming AdS_5. This is constructed as an asymptotically locally anti de Sitter (AlAdS) solution of five-dimensional minimal gauged supergravity, with topology R x R^4 and a non-trivial graviphoton field, and can be uplifted to ten or eleven dimensional supergravities. An analytic continuation of this solution yields the gravity dual to a class of four-dimensional N=1 supersymmetric gauge theories on a curved manifold with topology S^1 x S^3, comprising an SU(2) x U(1)-symmetric squashed three-sphere, with a non-trivial background gauge field coupling to the R-symmetry current. We compute the holographically renormalised on-shell action and interpret it in terms of the Casimir energy of the dual field theory. We also determine the holographic conserved charges of the solution and discuss relations between them.
6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Teschner, J.; Vartanov, G.S.
2012-02-15
We revisit the definition of the 6j-symbols from the modular double of U{sub q}(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories. (orig.)
6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
Teschner, J
2012-01-01
We revisit the definition of the 6j-symbols from the modular double of U_q(sl(2,R)), referred to as b-6j symbols. Our new results are (i) the identification of particularly natural normalization conditions, and (ii) new integral representations for this object. This is used to briefly discuss possible applications to quantum hyperbolic geometry, and to the study of certain supersymmetric gauge theories. We show, in particular, that the b-6j symbol has leading semiclassical asymptotics given by the volume of a non-ideal tetrahedron. We furthermore observe a close relation with the problem to quantize natural Darboux coordinates for moduli spaces of flat connections on Riemann surfaces related to the Fenchel-Nielsen coordinates. Our new integral representations finally indicate a possible interpretation of the b-6j symbols as partition functions of three-dimensional N=2 supersymmetric gauge theories.
Implications of non-universality of soft terms in supersymmetric grand unified theories
Matalliotakis, D
1994-01-01
Most discussions of supersymmetric grand unified theories assume universality of the soft supersymmetry breaking terms at the grand scale. We point out that the behaviour of these theories might change significantly in the presence of non--universal soft terms. Particularly in SO(10)--like models with a large value of tan\\beta we observe a decisive change of predictions, allowing the presence of relatively light gauginos as well as small supersymmetric corrections to the b--quark mass. Some results remain rather stable, including the \\mu--M_{1/2} correlation. Models with small tan\\beta seem to be less affected by non--universality which mainly leads to the new possibility of small m_{0} (i.e. the squark and slepton soft mass parameter), excluded in the universal case.
Hamiltonian methods in the theory of solitons
Fadeev, Ludwig
1987-01-01
The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrodinger equation is considered as a main example, forming the first part of the book. The second part examines such fundamental models as the sine-Gordon equation and the Heisenberg equation, the classification of integrable models and methods for constructing their solutions.
Supersymmetric Solutions in Three-Dimensional Heterotic String Theory
Bakas, Ioannis; Lópes-Cardoso, G; Bakas, Ioannis; Bourdeau, Michele; Cardoso, Gabriel Lopes
1998-01-01
We consider the low-energy effective field theory of heterotic string theory compactified on a seven-torus, and we construct electrically charged as well as more general solitonic solutions. These solutions preserve 1/2, 1/4, 1/8 and 1/16 of N=8, D=3 supersymmetry and have Killing spinors which exist due to cancellation of holonomies. The associated space-time line elements do not exhibit the conical structure that often arises in 2+1 dimensional gravity theories.
Natural realization of large extra dimension in 5D supersymmetric theory
Sakamura, Yutaka
2014-01-01
An exponentially large extra dimension can be naturally realized by the Casimir energy and the gaugino condensation in 5D supersymmetric theory. The model does not require any hierarchies among the 5D parameters. The key ingredient is an additional modulus other than the radion, which generically exists in 5D supergravity. SUSY is broken at the vacuum, which can be regarded as the Scherk-Schwarz SUSY breaking. We also analyze the mass spectrum and discuss some phenomenological aspects.
Cross-Order Relations in N=4 Supersymmetric Gauge Theories
Anastasiou, C; Dixon, L J; Kosower, D A
2004-01-01
The anti-de Sitter/conformal field theory duality conjecture raises the question of how the perturbative expansion in the conformal field theory can resum to a simple function. We exhibit a relation between the one-loop and two-loop amplitudes whose generalization to higher-point and higher-loop amplitudes would answer this question. We also provide evidence for the first of these generalizations.
N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
Dijkgraaf, R; Schroers, B J
1998-01-01
We study N=4 supersymmetric Yang-Mills theory on a Kaehler manifold with $b_2^+ \\geq 3$. Adding suitable perturbations we show that the partition function of the N=4 theory is the sum of contributions from two branches: (i) instantons, (ii) a special class of Seiberg-Witten monopoles. We determine the partition function for the theories with gauge group SU(2) and SO(3), using S-duality. This leads us to a formula for the Euler characteristic of the moduli space of instantons.
CHIRAL RING OF Sp(N) AND SO(N) SUPERSYMMETRIC GAUGE THEORY IN FOUR DIMENSIONS
Institute of Scientific and Technical Information of China (English)
E. WITTEN
2003-01-01
The chiral ring of classical supersymmetric Yang-Mills theory with gauge group Sp(N) or SO(N) is computed, extending previous work (of Cachazo, Douglas, Seiberg, and the author)for SU(N). The result is that, as has been conjectured, the ring is generated by the usualglueball superfield S ～ Tr WαWα, with the relation Sh = 0, h being the dual Coxeter number.Though this proposition has important implications for the behavior of the quantum theory,the statement and (for the most part) the proofs amount to assertions about Lie groups withno direct reference to gauge theory.
Geometry and off-shell nilpotency for N = 1 supersymmetric Yang-Mills theory
Meziane, A
2015-01-01
We show that for N = 1 supersymmetric Yang-Mills theory it is possible to build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST superspace formalism. This is based on the introduction of the basic fields of the quantized theory together with an auxiliary real field via the lowest components of the superfield components of a superYang-Mills connection. Here, the associated supercurvature is constrained by horizontality conditions as in ordinary Yang-Mills theory. We also show how the off-shell BRST-invariant quantum action can be constructed starting from a gauge-fixed superaction.
Solvable Relativistic Hydrogenlike System in Supersymmetric Yang-Mills Theory
DEFF Research Database (Denmark)
Caron-Huot, Simon; Henn, Johannes M.
2014-01-01
he classical Kepler problem, as well as its quantum mechanical version, the hydrogen atom, enjoys a well-known hidden symmetry, the conservation of the Laplace-Runge-Lenz vector, which makes these problems superintegrable. Is there a relativistic quantum field theory extension that preserves...... this symmetry? In this Letter we show that the answer is positive: in the nonrelativistic limit, we identify the dual conformal symmetry of planar N=4 super Yang-Mills theory with the well-known symmetries of the hydrogen atom. We point out that the dual conformal symmetry offers a novel way to compute...... the spectrum of bound states of massive W bosons in the theory. We perform nontrivial tests of this setup at weak and strong coupling and comment on the possible extension to arbitrary values of the coupling....
N=1 supersymmetric Yang-Mills theory on the lattice
Energy Technology Data Exchange (ETDEWEB)
Piemonte, Stefano
2015-04-08
Supersymmetry (SUSY) relates two classes of particles of our universe, bosons and fermions. SUSY is considered nowadays a fundamental development to explain many open questions about high energy physics. The N=1 super Yang-Mills (SYM) theory is a SUSY model that describes the interaction between gluons and their fermion superpartners called ''gluinos''. Monte Carlo simulations on the lattice are a powerful tool to explore the non-perturbative dynamics of this theory and to understand how supersymmetry emerges at low energy. This thesis presents new results and new simulations about the properties of N=1 SYM, in particular about the phase diagram at finite temperature.
N=1 Supersymmetric $SU(2)^r$ Moose Theories
Hailu, G
2003-01-01
We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial quantum moduli spaces and dynamical superpotentials are produced. When the moduli space is perturbed by generic tree level superpotentials, the vacuum space becomes discrete. The ring moose is in the Coulomb phase and we find two singular submanifolds with a nontrivial modulus that is a function of all the independent gauge invariants needed to parameterize the quantum moduli space. The massive theory near these singularities confines. The Seiberg-Witten elliptic curve that describes the quantum moduli space of the ring moose is produced.
Csáki, C; Csaki, Csaba; Randall, Lisa
1995-01-01
There are few robust solutions to the doublet-triplet splitting problem in supersymmetric GUT theories. One of the more promising solutions is the Higgs as pseudo-Goldstone boson mechanism. In its minimal implementation, such a solution places an additional restriction on the parameter space of the minimal supersymmetric standard model. A testable consequence of this constraint is an equation for \\tan \\beta. We present this restriction and study its solutions in order to constrain the allowed parameter space. Thus the assumptions on the GUT scale Higgs sector should yield testable predictions for weak scale physics. If the SUSY parameters are measured then it should be possible to check the predictions, yielding insight into GUT scale physics.
Transport properties of N = 4 supersymmetric Yang-Mills theory at finite coupling
Energy Technology Data Exchange (ETDEWEB)
Benincasa, Paolo [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Buchel, Alex [Department of Applied Mathematics, University of Western Ontario, Middlesex College, London, ON, N6A 5B7 (Canada); Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada)
2006-01-15
Gauge theory-string theory duality describes strongly coupled N = 4 supersymmetric SU(n{sub c}) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-n{sub c} N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order {alpha}'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the {alpha}'-corrected nonextremal black branes in string theory.
Transport properties of Script N = 4 supersymmetric Yang-Mills theory at finite coupling
Benincasa, Paolo; Buchel, Alex
2006-01-01
Gauge theory-string theory duality describes strongly coupled Script N = 4 supersymmetric SU(nc) Yang-Mills theory at finite temperature in terms of near extremal black 3-brane geometry in type IIB string theory. We use this correspondence to compute the leading correction in the inverse 't Hooft coupling to the shear diffusion constant, bulk viscosity and the speed of sound in the large-nc Script N = 4 supersymmetric Yang-Mills theory plasma. The transport coefficients are extracted from the dispersion relation of the shear and the sound wave lowest quasinormal modes in the leading order α'-corrected black D3 brane geometry. We find the shear viscosity extracted from the shear diffusion constant to agree with result of [hep-th/0406264]; also, the leading correction to bulk viscosity and the speed of sound vanishes. Our computation provides a highly nontrivial consistency check on the hydrodynamic description of the α'-corrected nonextremal black branes in string theory.
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
Marino, Marcos
2011-01-01
In these lectures I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N^{3/2} behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals, and large N techniques in matrix models
Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories
Mariño, Marcos
2011-11-01
In these lectures, I give a pedagogical presentation of some of the recent progress in supersymmetric Chern-Simons-matter theories, coming from the use of localization and matrix model techniques. The goal is to provide a simple derivation of the exact interpolating function for the free energy of ABJM theory on the three-sphere, which implies in particular the N3/2 behavior at strong coupling. I explain in detail part of the background needed to understand this derivation, like holographic renormalization, localization of path integrals and large N techniques in matrix models.
Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
Anastasiou, C; Dixon, L; Kosower, D A
2003-01-01
The collinear factorization properties of two-loop scattering amplitudes in dimensionally-regulated N=4 super-Yang-Mills theory suggest that, in the planar ('t Hooft) limit, higher-loop contributions can be expressed entirely in terms of one-loop amplitudes. We demonstrate this relation explicitly for the two-loop four-point amplitude and, based on the collinear limits, conjecture an analogous relation for n-point amplitudes. The simplicity of the relation is consistent with intuition based on the AdS/CFT correspondence that the form of the large N_c L-loop amplitudes should be simple enough to allow a resummation to all orders.
Lecture Notes on Three Supersymmetric/Topological Systems in Quantum Field Theory
Guilarte, Juan Mateos
2016-01-01
((1+1)-dimensional ${\\cal N}=1$ super-symmetric field theory and (3+1)-dimensional ${\\cal N}=2$ super-symmetric gauge theory are discussed in a, more or less, unified way, designed to identify the quantum BPS states in both systems. Euclidean 4-dimensional gauge theory with ${\\cal N}=2$ twisted super-symmetry is also analized. ${\\bf C}^\\infty$-topological invariants are identified as certain n-point correlation functions in this QFT framework. The twist of the effective dual Abelian gauge theory is briefly described, both from mathematical and physical viewpoints. The physical nature of the topological defects arising in these systems, kinks, BPS and Dirac monopoles, BPST instantons, Liouville and Abrikosov-Nielsen-Olesen selfdual vortices, etcetera, is analyzed, The thread of the story connecting the QFT systems treated respectively in Sections \\S.3 and \\S.4 is the process of TWIST that leads from a conventional extended Supersymetric Gauge Theory to the topological ${\\cal N}=2$ SUSY Donaldson QFT. Within Se...
Groot Nibbelink, Stefan; Parr, Erik
2016-08-01
Inspired by the tachyon-free nonsupersymmetric heterotic SO (16 )×SO (16 ) string we consider a special class of nonsupersymmetric field theories: those that can be obtained from supersymmetric field theories by supersymmetry-breaking twists. We argue that such theories, like their supersymmetric counterparts, may still possess some fermionic symmetries as leftovers of the supergauge transformations and have special one-loop nonrenormalization properties due to holomorphicity. In addition, we extend the supergraph techniques to these theories to calculate some explicit supersymmetry-breaking corrections.
Instanton calculus and chiral one-point functions in supersymmetric gauge theories
Fujii, S; Moriyama, S; Okada, S; Fujii, Shigeyuki; Kanno, Hiroaki; Moriyama, Sanefumi; Okada, Soichi
2007-01-01
We compute topological one-point functions of the chiral operator Tr (\\phi^k) in the maximally confining phase of N=1 U(N) supersymmetric gauge theory, which is obtained from N=2 theory by turning on a tree level superpotential W(\\Phi). Localization theorem for toric action allows us to express these one-point functions as polynomials in the equivariant parameter \\hbar and the parameter of instanton expansion q=\\Lambda^{2N}. The chiral one-point functions are of particular interest from gauge/string theory correspondence, since they are related to the Gromov-Witten theory of P^1. Based on a combinatorial identity that gives summation formula over Young diagram of relevant functions, we find a relation among chiral one-point functions, which recursively determines the \\hbar expansion of the generating function of one-point functions.
Supersymmetric grand unified theories from quarks to strings via SUSY GUTs
Raby, Stuart
2017-01-01
These course-tested lectures provide a technical introduction to Supersymmetric Grand Unified Theories (SUSY GUTs), as well as a personal view on the topic by one of the pioneers in the field. While the Standard Model of Particle Physics is incredibly successful in describing the known universe it is, nevertheless, an incomplete theory with many free parameters and open issues. An elegant solution to all of these quandaries is the proposed theory of SUSY GUTs. In a GUT, quarks and leptons are related in a simple way by the unifying symmetry and their electric charges are quantized, further the relative strength of the strong, weak and electromagnetic forces are predicted. SUSY GUTs additionally provide a framework for understanding particle masses and offer candidates for dark matter. Finally, with the extension of SUSY GUTs to string theory, a quantum-mechanically consistent unification of the four known forces (including gravity) is obtained. The book is organized in three sections: the first section contai...
Three-loop octagons and n-gons in maximally supersymmetric Yang-Mills theory
DEFF Research Database (Denmark)
Caron Huot, Simon; He, Song
2013-01-01
, the higher-point amplitudes we consider can be obtained from those with lowest-points by a collinear uplifting. Based on a compact formula for one-loop N(2)MHV amplitudes, we use an equation proposed previously to compute, for the first time, the complete two-loop NMHV and three-loop MHV octagons, which we......We study the S-matrix of planar = 4 supersymmetric Yang-Mills theory when external momenta are restricted to a two-dimensional subspace of Minkowski space. We find significant simplifications and new, interesting structures for tree and loop amplitudes in two-dimensional kinematics, in particular...
N=4 Supersymmetric Yang-Mills Theory on Orbifold-$T^4/{\\bf Z}_2$
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of N=4 supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$. In classical geometry, K3 surface is constructed from the orbifold-$T^4/{\\bf Z}_2$. Along the same way as the orbifold construction, we construct the partition function of K3 surface from orbifold-$T^4/{\\bf Z}_2$. The partition function is given by the product of the contribution of the untwisted sector of $T^4/{\\bf Z}_2$, and that of the twisted sector of $T^4/{\\bf Z}_2$ i.e., ${\\cal O}(-2)$ curve blow-up formula.
General N=1 supersymmetric flux vacua of massive type IIA string theory.
Behrndt, Klaus; Cvetic, Mirjam
2005-07-08
We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.
Lepton flavor violating process in a supersymmetric grand unified theory with right-handed neutrino
Baek, S; Okada, Y; Okumura, K; Baek, Seungwon; Goto, Toru; Okada, Yasuhiro; Okumura, Ken-ichi
2001-01-01
Motivated from the recent results of neutrino oscillation experiment, we investigated lepton flavor violating (LFV) processes in a SU(5) supersymmetric grand unified theory with right-handed neutrino. The current experimental upper bound for $\\mu \\to e\\gamma$ process gives already some constraint on the model. Correlation between $\\mu \\to e \\gamma$ and the SUSY contribution to the muon anomalous magnetic moment is also discussed. Future LFV experiments will give considerable impacts on this type of SUSY GUT models equipped with seesaw neutrino mass generation.
Lepton flavor-violating process in a supersymmetric grand unified theory with right-handed neutrinos
Energy Technology Data Exchange (ETDEWEB)
Baek, Seungwon; Goto, Toru; Okada, Yasuhiro; Okumura, Ken-ichi E-mail: okumurak@icrr.u-tokyo.ac.jp
2003-05-01
Motivated by the recent results of neutrino oscillation experiments, we investigated lepton flavor-violating (LFV) processes in a SU(5) supersymmetric grand unified theory with right-handed neutrinos. The current experimental upper bound for the {mu}{yields}e{gamma} process already gives some constraint on the model. The correlation between {mu}{yields}e{gamma} and the SUSY contribution to the muon anomalous magnetic moment is also discussed. Future LFV experiments will have considerable impacts on this type of SUSY GUT model equipped with seesaw neutrino mass generation.
D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
Bern, Zvi; Dixon, Lance J.; Douglas, Michael R.; von Hippel, Matt; Johansson, Henrik
2013-01-01
The connection of maximally supersymmetric Yang-Mills theory to the (2,0) theory in six dimensions has raised the possibility that it might be perturbatively ultraviolet finite in five dimensions. We test this hypothesis by computing the coefficient of the first potential ultraviolet divergence of planar (large $N_c$) maximally supersymmetric Yang-Mills theory in D = 5, which occurs at six loops. We show that the coefficient is nonvanishing. Furthermore, the numerical value of the divergence falls very close to an approximate exponential formula based on the coefficients of the divergences through five loops. This formula predicts the approximate values of the ultraviolet divergence at loop orders L > 6 in the critical dimension D = 4 + 6/L. To obtain the six-loop divergence we first construct the planar six-loop four-point amplitude integrand using generalized unitarity. The ultraviolet divergence follows from a set of vacuum integrals, which are obtained by expanding the integrand in the external momenta. T...
Comparison of Some Exact and Perturbative Results for a Supersymmetric SU($N_c$) Gauge Theory
DEFF Research Database (Denmark)
Ryttov, Thomas; Shrock, Robert
2012-01-01
We consider vectorial, asymptotically free ${\\cal N}=1$ supersymmetric SU($N_c$) gauge theories with $N_f$ copies of massless chiral super fields in various representations and study how perturbative predictions for the lower boundary of the infrared conformal phase, as a function of $N_f$, compare...... S_2$, and (iv) $A_2 + \\bar A_2$, where $F$, $Adj$, $S_2$, and $A_2$ denote, respectively, the fundamental, adjoint, and symmetric and antisymmetric rank-2 tensor representations. We find that perturbative results slightly overestimate the value of $N_{f,cr}$ relative to the respective exact results...... for these representations, i.e., slightly underestimate the interval in $N_f$ for which the theory has infrared conformal behavior. Our results provide a measure of how closely perturbative calculations reproduce exact results for these theories....
Khoury, Justin; Ovrut, Burt A
2011-01-01
Galileon theories are of considerable interest since they allow for stable violations of the null energy condition. Since such violations could have occurred during a high-energy regime in the history of our universe, we are motivated to study supersymmetric extensions of these theories. This is carried out in this paper, where we construct generic classes of N=1 supersymmetric Galileon Lagrangians. They are shown to admit non-equivalent stress-energy tensors and, hence, vacua manifesting differing conditions for violating the null energy condition. The temporal and spatial fluctuations of all component fields of the supermultiplet are analyzed and shown to be stable on a large number of such backgrounds. In the process, we uncover a surprising connection between conformal Galileon and ghost condensate theories, allowing for a deeper understanding of both types of theories.
Supersymmetric Open Wilson Lines
Baker, Edward B
2011-01-01
In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.
The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere
Energy Technology Data Exchange (ETDEWEB)
Martelli, Dario, E-mail: dario.martelli@kcl.ac.uk [Department of Mathematics, King' s College, London, The Strand, London WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)
2013-01-01
We present the gravity dual to a class of three-dimensional N=2 supersymmetric gauge theories on a biaxially squashed three-sphere, with a non-trivial background gauge field. This is described by a 1/2 BPS Euclidean solution of four-dimensional N=2 gauged supergravity, consisting of a Taub-NUT-AdS metric with a non-trivial instanton for the graviphoton field. The holographic free energy of this solution agrees precisely with the large N limit of the free energy obtained from the localized partition function of a class of Chern-Simons quiver gauge theories. We also discuss a different supersymmetric solution, whose boundary is a biaxially squashed Lens space S{sup 3}/Z{sub 2} with a topologically non-trivial background gauge field. This metric is of Eguchi-Hanson-AdS type, although it is not Einstein, and has a single unit of gauge field flux through the S{sup 2} cycle.
High energy behavior of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bartels, Jochen; Hentschinski, Martin; Mischler, Anna-Maria [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik; Ewerz, Carlo [Heidelberg Univ. (Germany). Inst. fuer Theoretische Physik; GSI Helmholtzzentrum fuer Schwerionenforschung, Darmstadt (Germany). ExtreMe Matter Institute EMMI; Bielefeld Univ. (Germany). Fakultaet fuer Physik; European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT), Villazzano (Italy)
2009-12-15
We study the high energy limit of a six-point R-current correlator in N=4 supersymmetric Yang-Mills theory for finite N{sub c}. We make use of the framework of perturbative resummation of large logarithms of the energy. More specifically, we apply the (extended) generalized leading logarithmic approximation. We find that the same conformally invariant two-to-four gluon vertex occurs as in non-supersymmetric Yang-Mills theory. As a new feature we find a direct coupling of the four-gluon t-channel state to the R-current impact factor. (orig.)
Supersymmetric Yang Mills Fields and Black Holes ; In Ten Dimensional Unified Field Theory
Patwardhan, Ajay
2007-01-01
The Ten dimensional Unified field theory has a 4 dimensional Riemannian spacetime and six dimensional Calabi Yau space structure. The supersymmetric Yang Mills fields and black holes are solutions in these theories. The formation of primordial black holes in early universe, the collapse to singularity of stellar black holes, the Hawking evaporation of microscopic black holes in LHC are topics of observational and theoretical interest. The observation of gamma ray bursts and creation of spectrum of particles and radiation of dark and normal matter occur due to primordial and microscopic black holes. The approach to singularity in black hole interior solutions, require the Bogoliubov transforms of SUSY YM fields in black hole geometries; both during formation and in evaporation. The Hawking effect of radiating black holes is applicable for all the fields. Invariants can be defined to give the conditions for these processes.
Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory
Koloğlu, Murat
2016-01-01
We analyze the classical and quantum vacua of 2d $\\mathcal{N}=(8,8)$ supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group, describing the worldvolume interactions of $N$ parallel D1-branes with flat transverse directions $\\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$ theory in the superselection sector labeled $M \\pmod{N}$ --- identified with the internal dynamics of $(M,N)$-string bound states of Type IIB string theory --- is described by the symmetric orbifold $\\mathcal{N}=(8,8)$ sigma model into $(\\mathbb{R}^8)^{D-1}/\\mathbb{S}_D$ when $D=\\gcd(M,N)>1$, and by a single massive vacuum when $D=1$, generalizing the conjectures of E. Witten and others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with an additional $U(1)$ 2-form gauge field $B$ coming from the string theory Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations, labeled by the $\\mathbb{Z}$-valued generalized electric flux and an independent $\\mathbb{Z}_N$-valued 't Hooft flux...
Reflection of sine-Gordon breathers
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1981-01-01
The influence of a boundary on a breather traveling in a Josephson line cavity is examined by means of numerical computations. For a passive termination the breather is reflected into a breather of less energy; when the characteristic impedance of the line equals the external load resistor the br...
Oscillating and rotating sine-Gordon system
DEFF Research Database (Denmark)
Olsen, O. H.; Samuelsen, Mogens Rugholm
1986-01-01
on the rate of change of the vacuum. For small rates a parametric excitation of standing waves is found, and for larger rates the system linearizes. In the case of oscillating vacuum a perturbation approach explains the behavior perfectly, while for small rates of increasing vacuum the system reduces...
Barranco, Alejandro
2012-01-01
We implement relativistic BCS superconductivity in N=1 supersymmetric field theories with a U(1)_R symmetry. The simplest model contains two chiral superfields with a Kahler potential modified by quartic terms. We study the phase diagram of the gap as a function of the temperature and the specific heat. The superconducting phase transition turns out to be first order, due to the scalar contribution to the one-loop potential. By virtue of supersymmetry, the critical curves depend logarithmically with the UV cutoff, rather than quadratically as in standard BCS theory. We comment on the difficulties in having fermion condensates when the chemical potential is instead coupled to a baryonic U(1)_B current. We also discuss supersymmetric models of BCS with canonical Kahler potential constructed by "integrating-in" chiral superfields.
Framed sheaves on root stacks and supersymmetric gauge theories on ALE spaces
Bruzzo, Ugo; Sala, Francesco; Szabo, Richard J
2016-01-01
We develop a new approach to the study of supersymmetric gauge theories on ALE spaces using the theory of framed sheaves on root toric stacks, which illuminates relations with gauge theories on $\\mathbb{R}^4$ and with two-dimensional conformal field theory. We construct a stacky compactification of a minimal resolution $X_k$ of the $A_{k-1}$ toric singularity $\\mathbb{C}^2/\\mathbb{Z}_k$, which is a projective toric orbifold $\\mathscr{X}_k$ such that $\\mathscr{X}_k\\setminus X_k$ is a $\\mathbb{Z}_k$-gerbe. We construct moduli spaces of torsion free sheaves on $\\mathscr{X}_k$ which are framed along the compactification gerbe. We prove that this moduli space is a smooth quasi-projective variety, compute its dimension, and classify its fixed points under the natural induced toric action. We use this construction to compute the partition functions and correlators of chiral BPS operators for $\\mathcal{N}=2$ quiver gauge theories on $X_k$ with nontrivial holonomies at infinity. The partition functions are computed wi...
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Özugurel, Umut D; Sandbrink, Dirk
2013-01-01
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-eta-prime, the a-f0 meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua
Cassani, Davide; Varela, Oscar
2012-01-01
We study consistent truncations of M-theory to gauged N=2 supergravity in four dimensions, based on a large class of SU(3)-structures in seven dimensions. We show that the gauging involves isometries of the vector multiplet scalar manifold as well as the Heisenberg algebra and a special isometry of the hyperscalar manifold. As a result, non-abelian gauge groups and new non-trivial scalar potentials are generated. Then we specialize to all homogeneous SU(3)-structures supporting supersymmetric AdS4 vacua. These are the Stiefel manifold V52, the Aloff-Wallach spaces N(k,l), the seven-sphere (seen as SU(4)/SU(3) or Sp(2)/Sp(1)) and the M110 and Q111 coset spaces. For each of these cases, we describe in detail the N=2 model and discuss its peculiarities.
Towards the spectrum of low-lying particles in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Bergner, G. [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Montvay, I. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Muenster, G.; Oezugurel, U.D.; Sandbrink, D. [Muenster Univ. (Germany). Inst. fuer Theoretische Physik 1
2013-04-15
We present the current results of our simulations of N=1 supersymmetric Yang-Mills theory on a lattice. The masses of the gluino-glue particle, the a-{eta}', the a-f{sub 0} meson, and the scalar glueball are obtained at finer lattice spacing than before, and extrapolations towards vanishing gluino mass are made. The calculations employ different levels of stout smearing. The statistical accuracy as well as the control of finite size effects and lattice artefacts are better than in previous investigations. Taking the statistical and systematic uncertainties into account, the extrapolations towards vanishing gluino mass of the masses of the fermionic and bosonic states in our present calculations are consistent with the formation of degenerate supermultiplets.
Third generation effects on fermion mass predictions in supersymmetric grand unified theories
Naculich, S G
1993-01-01
Relations among fermion masses and mixing angles at the scale of grand unification are modified at lower energies by renormalization group running induced by gauge and Yukawa couplings. In supersymmetric theories, the $b$ quark and $\\tau$ lepton Yukawa couplings, as well as the $t$ quark coupling, may cause significant running if $\\tan \\beta$, the ratio of Higgs field expectation values, is large. We present approximate analytic expressions for the scaling factors for fermion masses and CKM matrix elements induced by all three third generation Yukawa couplings. We then determine how running caused by the third generation of fermions affects the predictions arising from three possible forms for the Yukawa coupling matrices at the GUT scale: the Georgi-Jarlskog, Giudice, and Fritzsch textures.
Dirichlet branes and nonperturbative aspects of supersymmetric string and gauge theories
Energy Technology Data Exchange (ETDEWEB)
Yin, Zheng [Univ. of California, Berkeley, CA (United States)
1998-05-01
In chapter 1 the author reviews some elements of string theory relevant to the rest of this report. He touches on both the classical, i.e. perturbative, string physics before D-branes rise to prominence, and some of the progresses they brought forth. In chapter 2 he proceeds to give an exact algebraic formulation of D-branes in curved spaces. This allows one to classify them in backgrounds of interest and study their geometric properties. He applies this formalism to string theory on Calabi-Yau and other supersymmetry preserving manifolds. Then he studies the behavior of the D-branes under mirror symmetry in chapter 3. Mirror symmetry is known to be a symmetry of string theory perturbatively. He finds evidence for its nonperturbative validity when D-branes are also considered and compute some dynamical consequences. In chapter 4 he turns to examine the consistency of curved and/or intersecting D-brane configurations. They have been used recently to extract information about the field theories that arise in certain limits. It turns out that there are potential quantum mechanical inconsistencies associated with them. What saves the day are certain subtle topological properties of D-branes. This resolution has implications for the conserved charges carried by the D-branes, which he computes for the cases studied in chapter 2. In chapter 5 he uses intersecting brane configurations to study three dimensional supersymmetric gauge theories. There is also a mirror symmetry there that, among other things, exchanges classical and quantum mechanical quantities of a (mirror) pair of theories. It has an elegant realization in term of a symmetry of string theory involving D-branes. The author employs it to study a wide class of 3d models. He also predicts new mirror pairs and unconventional 3d field theories without Lagrangian descriptions.
N=2,4 Supersymmetric Gauge Field Theory in 2T-physics
Bars, Itzhak
2008-01-01
In the context of Two Time Physics in 4+2 dimensions we construct the most general N=2,4 supersymmetric Yang Mills gauge theories for any gauge group G. This builds on our previous work for N=1 supersymmetry. The action, the conserved SUSY currents, and the off-shell SU(N) covariant SUSY transformation laws are presented for both N=2 and N=4. The on-shell SUSY transformations close to the supergroup SU(2,2$|$N) with N=1,2,4. The SU(2,2)=SO(4,2) sub-symmetry is realized linearly on 4+2 dimensional flat spacetime. All fields, including vectors and spinors, are in 4+2 dimensions. The extra gauge symmetries in 2T field theory, together with the kinematic constraints that follow from the action, remove all the ghosts to give a unitary theory. By choosing gauges and solving the kinematic equations, the 2T field theory in 4+2 flat spacetime can be reduced to various shadows in various 3+1 dimensional (generally curved) spacetimes. These shadows are related to each other by dualities. The conformal shadows of our the...
The gluino-glue particle and relevant scales for the simulations of supersymmetric Yang-Mills theory
Bergner, Georg; Münster, Gernot; Sandbrink, Dirk; Özugurel, Umut D
2012-01-01
Supersymmetric Yang-Mills theory is in several respects different from QCD and pure Yang-Mills theory. Therefore, a reinvestigation of the scales, at which finite size effects and lattice artifacts become relevant, is necessary. Both, finite size effects and lattice artifacts, induce a breaking of supersymmetry. In view of the unexpected mass gap between bosonic and fermionic particles an estimation of these effects is essential.
Effective World-Sheet Theory for Non-Abelian Semilocal Strings in N = 2 Supersymmetric QCD
Shifman, M; Yung, A
2011-01-01
We consider non-Abelian semilocal strings (vortices, or vortex-strings) arising in N=2 supersymmetric U(N) gauge theory with Nf=N+\\~N matter hypermultiplets in the fundamental representation (quarks), and a Fayet-Iliopoulos term {\\xi}. We present, for the first time ever, a systematic field-theoretic derivation of the world-sheet theory for such strings, describing dynamics of both, orientational and size zero modes. Our derivation is complete in the limit, ln(L)\\rightarrow \\infty, where L is an infrared (IR) regulator in the transverse plane. In this limit the world-sheet theory is obtained exactly. It is presented by a so far unknown N=2 two-dimensional sigma model, to which we refer as the zn model, with or without twisted masses. Alternative formulations of the zn model are worked out: conventional and extended gauged formulations and a geometric formulation. We compare the exact metric of the zn model with that of the weighted CP(Nf-1) model conjectured by Hanany and Tong, through D-branes, as the world-...
Energy Technology Data Exchange (ETDEWEB)
Kanemura, Shinya; Machida, Naoki [Department of Physics, University of Toyama, 3190 Gofuku, Toyama 930-8555 (Japan); Shindou, Tetsuo [Division of Liberal-Arts, Kogakuin University, 1-24-2 Nishi-Shinjuku, Tokyo 163-8677 (Japan)
2014-11-10
We propose a simple model to explain neutrino mass, dark matter and baryogenesis based on the extended Higgs sector which appears in the low-energy effective theory of a supersymmetric gauge theory with confinement. We here consider the SU(2){sub H} gauge symmetry with three flavours of fundamental representations which are charged under the standard SU(3){sub C}×SU(2){sub L}×U(1){sub Y} symmetry and a new discrete Z{sub 2} symmetry. We also introduce a Z{sub 2}-odd right-handed neutrino superfield in addition to the standard model matter superfields. The low-energy effective theory below the confinement scale contains the Higgs sector with fifteen composite superfields, some of which are Z{sub 2}-odd. When the confinement scale is of the order of ten TeV, electroweak phase transition can be sufficiently of first order, which is required for successful electroweak baryogenesis. The lightest Z{sub 2}-odd particle can be a new candidate for dark matter, in addition to the lightest R-parity odd particle. Neutrino masses and mixings can be explained by the quantum effects of Z{sub 2}-odd fields via the one-loop and three-loop diagrams. We find a benchmark scenario of the model, where all the constraints from the current neutrino, dark matter, lepton flavour violation and LHC data are satisfied. Predictions of the model are shortly discussed.
Kanemura, Shinya; Shindou, Tetsuo
2014-01-01
We propose a simple model to explain neutrino mass, dark matter and baryogenesis based on the extended Higgs sector which appears in the low-energy effective theory of a supersymmetric gauge theory with confinement. We here consider the SU(2)$_H$ gauge symmetry with three flavours of fundamental representations which are charged under the standard SU(3)$_C\\times$ SU(2)$_L\\times$U(1)$_Y$ symmetry and a new discrete $Z_2$ symmetry. We also introduce $Z_2$-odd right-handed neutrino superfields in addition to the standard model matter superfields. The low-energy effective theory below the confinement scale contains the Higgs sector with fifteen composite superfields, some of which are $Z_2$-odd. When the confinement scale is of the order of ten TeV, electroweak phase transition can be sufficiently of first order, which is required for successful electroweak baryogenesis. The lightest $Z_2$-odd particle can be a new candidate for dark matter, in addition to the lightest $R$-parity odd particle. Neutrino masses and...
Energy Technology Data Exchange (ETDEWEB)
Kord, A.F., E-mail: afarzaneh@hsu.ac.ir [Department of Physics, Hakim Sabzevari University (HSU), P.O. Box 397, Sabzevar (Iran, Islamic Republic of); Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531, Tehran (Iran, Islamic Republic of); Haddadi Moghaddam, M. [Department of Physics, Hakim Sabzevari University (HSU), P.O. Box 397, Sabzevar (Iran, Islamic Republic of)
2014-04-15
We study one loop corrections to N=1/2 supersymmetric SU(N)×U(1) pure gauge theory. We calculate divergent contributions of the 1PI graphs that contain the non-anti-commutative parameter C up to one loop corrections. We find that the disagreement between component formalism and superspace formalism is because of the field redefinition in component case. We modify gaugino field redefinition and lagrangian. We show that extra terms of lagrangian have been generated by λ redefinition and are necessary for the renormalisation of the theory. Finally we prove that N=1/2 supersymmetric gauge theory is renormalisable up to one loop corrections using standard method of renormalisation.
Picard-Fuchs Ordinary Differential Systems in $N = 2$ Supersymmetric Yang-Mills Theories
Ohta, Y
1999-01-01
In general, Picard-Fuchs systems in N=2 supersymmetric Yang-Mills theories are realized as a set of simultaneous partial differential equations. However, if the QCD scale parameter is used as unique independent variable instead of moduli, the resulting Picard-Fuchs systems are represented by a single ordinary differential equation (ODE) whose order coincides with the total number of independent periods. This paper discusses some properties of these Picard-Fuchs ODEs. In contrast with the usual Picard-Fuchs systems written in terms of moduli derivatives, there exists a Wronskian for this ordinary differential system and this Wronskian produces a new relation among periods, moduli and QCD scale parameter, which in the case of SU(2) is reminiscent of scaling relation of prepotential. On the other hand, in the case of the SU(3) theory, there are two kinds of ordinary differential equations, one of which is the equation directly constructed from periods and the other is derived from the SU(3) Picard-Fuchs equation...
Non-Abelian 1-Form Gauge Theory With Dirac Fields: Supersymmetric Unitary Operator
Bhanja, T; Malik, R P
2015-01-01
Within the framework of augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the supersymmetric (SUSY) unitary operator (and its hermitian conjugate) in the context of four (3 + 1)-dimensional (4D) interacting non-Abelian 1-form gauge theory with Dirac fields. The ordinary 4D non-Abelian theory, defined on the flat 4D Minkowski spacetime manifold, is generalized onto a (4, 2)-dimensional supermanifold which is parameterized by the spacetime bosonic coordinates x^\\mu (with \\mu = 0, 1, 2, 3) and a pair of Grassmannian variables (\\theta, \\bar\\theta) which satisfy the standard relationships: \\theta^2 = {\\bar\\theta}^2 = 0, \\theta\\,\\bar\\theta + \\bar\\theta\\,\\theta = 0. Various consequences of the application of the above SUSY unitary operator (and its hermitian conjugate) are discussed. In particular, we obtain the results of the application of the horizontality condition (HC) and gauge invariant restriction (GIR) in the language of the above SUSY operators. One of the no...
Lagrangian higher spin field theories from the O(N) extended supersymmetric particle
Marnelius, Robert
2009-01-01
The wave function in the quantum theory of the O(N) extended supersymmetric particle model describes a massless free field with spin N/2. This quantum theory is here exactly solved in terms of gauge fields in arbitrary even dimensions using only the basic quantum operators which include graded external differentials, trace operators, index structure operators and their duals. The resulting equations for the gauge fields are of first (N odd) or second order (N even) and are shown to be generalized (Fang)-Fronsdal equations which are fully gauge invariant since they include compensator fields in a natural way. Local gauge invariant actions are first derived in analogy with the derivation by Francia and Sagnotti in the symmetric case. Then a minimal formulation is given within which it is easy to set up gauge invariant actions and here appropriate actions for the above equations are proposed. In a second part it is shown that there exist projection operators from the states of the field strengths (wave functions...
Gürdoǧan, Ömer; Kazakov, Vladimir
2016-11-01
We introduce a family of new integrable quantum field theories in four dimensions by considering the γ -deformed N =4 supersymmetric Yang-Mills (SYM) theory in the double scaling limit of large imaginary twists and small coupling. This limit discards the gauge fields and retains only certain Yukawa and scalar interactions with three arbitrary effective couplings. In the `t Hooft limit, these 4D theories are integrable, and contain a wealth of conformal correlators such that the whole arsenal of AdS /CFT integrability remains applicable. As a special case of these models, we obtain a quantum field theory of two complex scalars with a chiral, quartic interaction. The Berenstein-Maldacena-Nastase vacuum anomalous dimension is dominated in each loop order by a single "wheel" graph, whose bulk represents an integrable "fishnet" graph. This explicitly demonstrates the all-loop integrability of gamma-deformed planar N =4 SYM theory, at least in our limit. Using this feature and integrability results we provide an explicit conjecture for the periods of double-wheel graphs with an arbitrary number of spokes in terms of multiple zeta values of limited depth.
Non-supersymmetric flux compactifications of heterotic string- and M-theory
Energy Technology Data Exchange (ETDEWEB)
Held, Johannes Georg Joseph
2012-05-08
This dissertation is concerned with non-supersymmetric vacua of string theory in the supergravity (SUGRA) approach. This approach is the effective description of string theory at low energies. The concrete field of research that is treated here is heterotic E{sub 8} x E{sub 8} string theory at weak and at strong coupling, respectively. In the strong coupling limit the theory is described by eleven-dimensional SUGRA with two ten-dimensional boundaries (heterotic M-Theory). The transition to the weak coupling limit is governed by the restricted space dimension, whose length tends to zero for weak coupling such that the two boundaries get identified with each other. The resulting theory is ten-dimensional E{sub 8} x E{sub 8} SUGRA. In the context of this heterotic SUGRA, at first six of the former nine space-dimensions are compactified, and then, in the presence of non-vanishing background flux, conditions for unbroken supersymmetry (SUSY) in four space-time dimensions are analyzed. Afterwards, a violation of one of the necessary SUSY conditions is allowed. An essential ingredient, necessary for this to work, is the presence of flux. This kind of SUSY-breaking leads to severe constraints on the compact six-dimensional manifold, which can be satisfied by fiber bundles with two-dimensional fiber and four-dimensional base. In simple examples one can stabilize the expectation value of the dilaton as well as the volume of the fiber, whereas the volume of the base remains undetermined. Furthermore, the effect of a fermionic condensate is analyzed. The expected additional SUSY-breaking can be observed, and it is shown that the breaking induced by the flux can not be canceled by the contributions from the condensate. The end of this thesis is concerned with the discussion of the strong coupling limit of the previously found examples. To analyze this, it is necessary to rewrite the action of heterotic M-theory as a sum of quadratic terms, which vanish once SUSY is imposed
${\\cal N}=4$ Supersymmetric Yang-Mills Theory on Orbifold-$T^4\\/{\\bf Z}_$2 Higher Rank Case
Jinzenji, M; Jinzenji, Masao; Sasaki, Toru
2001-01-01
We derive the partition function of ${\\cal N}=4$ supersymmetric Yang-Mills theory on orbifold-$T^4/{\\bf Z}_2$ for SU(N). We generalize our previous work for SU(2) to the SU(N) case. These partition functions can be factorized into product of bulk contribution of quotient space $T^4/{\\bf Z}_2$ and of blow-up formula including $A_{N-1}$ theta functions with level N.
Konishi form factor at three loops in N =4 supersymmetric Yang-Mills theory
Ahmed, Taushif; Banerjee, Pulak; Dhani, Prasanna K.; Rana, Narayan; Ravindran, V.; Seth, Satyajit
2017-04-01
We present the first results on the third order corrections to on-shell form factor (FF) of the Konishi operator in N =4 supersymmetric Yang-Mills theory using Feynman diagrammatic approach in modified dimensional reduction (D R ¯ ) scheme. We show that it satisfies the KG equation in D R ¯ scheme while the result obtained in four dimensional helicity (FDH) scheme needs to be suitably modified not only to satisfy the KG equation but also to get the correct ultraviolet (UV) anomalous dimensions. We find that the cusp, soft and collinear anomalous dimensions obtained to third order are same as those of the FF of the half-BPS operator confirming the universality of the infrared (IR) structures of on-shell form factors. In addition, the highest transcendental terms of the FF of the Konishi operator are identical to those of half-BPS operator indicating the probable existence of deeper structure of the on-shell FF. We also confirm the UV anomalous dimensions of the Konishi operator up to third order providing a consistency check on the both UV and universal IR structures in N =4 .
Supersymmetric gauge theories, quantization of M{sub flat}, and conformal field theory
Energy Technology Data Exchange (ETDEWEB)
Teschner, J.; Vartanov, G.S.
2013-02-15
We propose a derivation of the correspondence between certain gauge theories with N=2 supersymmetry and conformal field theory discovered by Alday, Gaiotto and Tachikawa in the spirit of Seiberg-Witten theory. Based on certain results from the literature we argue that the quantum theory of the moduli spaces of flat SL(2,R)-connections represents a nonperturbative ''skeleton'' of the gauge theory, protected by supersymmetry. It follows that instanton partition functions can be characterized as solutions to a Riemann-Hilbert type problem. In order to solve it, we describe the quantization of the moduli spaces of flat connections explicitly in terms of two natural sets of Darboux coordinates. The kernel describing the relation between the two pictures represents the solution to the Riemann Hilbert problem, and is naturally identified with the Liouville conformal blocks.
(2,2) and (0,4) Supersymmetric Boundary Conditions in 3d N = 4 Theories and Type IIB Branes
Chung, Hee-Joong
2016-01-01
The half-BPS boundary conditions preserving N = (2,2) and N = (0,4) supersymmetry in 3d N = 4 supersymmetric gauge theories are examined. The BPS equations admit decomposition of the bulk supermultiplets into specific boundary supermultiplets of preserved supersymmetry. Bogomolony-like equations and Nahm-like equations arise in the vector multiplet BPS boundary conditions and Robin-type boundary conditions appear for the hypermultiplet coupled to vector multiplet. The half-BPS boundary conditions are realized in the brane configurations of Type IIB string theory.
Supersymmetric Color Superconductivity
Harnik, R; Murayama, H; Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi
2004-01-01
Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N_c) gauge theories with N_f flavors of quarks in the presence of a baryon chemical potential mu, and describe the global symmetry breaking patterns at low energy. Our analysis requires mu mu_c. We also give a qualitative description of the phases in the `conformal window', 3/2 N_c < N_f < 3N_c, at finite density.
Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories.
Honda, Masazumi
2016-05-27
We study weak coupling perturbative series in 4D N=2 and 5D N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N=2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.
Instantons in four-Fermi term broken supersymmetric quantum mechanics with general potential
Energy Technology Data Exchange (ETDEWEB)
Hatzinikitas, Agapitos; Smyrnakis, Ioannis [University of Crete, Department of Applied Mathematics, L. Knosou-Ambelokipi, 71409 Iraklio, Crete (Greece)
2004-01-09
We have shown here how to find an integral representation for the solution of the Euclidean equations of motion of a quantum mechanical point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points {tau} {yields} {+-} {infinity}. As an application, the quantum mechanical sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.
Supersymmetric color superconductivity
Energy Technology Data Exchange (ETDEWEB)
Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi
2003-09-18
Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N{sub c}) gauge theories with N{sub f} flavors of quarks in the presence of a baryon chemical potential {mu}, and describe the global symmetry breaking patterns at low energy. Our analysis requires {mu} < {Lambda} and is thus complementary to the variational approach that has been successful for {mu} >> {Lambda}. We find that for N{sub F} < N{sub c} a modified U(1){sub B} symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N{sub f} = N{sub c} there is a critical chemical potential above which the U(1){sub B} is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N{sub c} + 1 {le} N{sub f} < 3/2 N{sub c} and find that baryon number is broken dynamically for {mu} > {mu}{sub c}. We also give a qualitative description of the phases in the ''conformal window'', 3/2 N{sub c} < N{sub f} < 3N{sub c}, at finite density.
A Complete Analysis of "Flavored" Electric Dipole Moments in Supersymmetric Theories
Hisano, Junji; Nagai, Minoru; Paradisi, Paride
2008-01-01
The Standard Model predictions for the hadronic and leptonic electric dipole moments (EDMs) are well far from the present experimental resolutions, thus, the EDMs represent very clean probes of New Physics effects. Especially, within supersymmetric frameworks with flavor-violating soft terms large and potentially visible effects to the EDMs are typically expected. In this work, we systematically evaluate the predictions for the EDMs at the beyond-leading-order (BLO). In fact, we show that BLO...
Space & time discontinuities in Liouville theory and its discrete analogue
Doikou, Anastasia
2016-01-01
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evolution of the defect degrees of freedom are determined, found in the form of the local equations of motion. We also revisit the continuous Liouville theory, deriving its local integrals of motion and comparing these with previous results from the sine-Gordon point of view.Finally, the generic Backlund type relations are presented, corresponding to the implementation of time-like and space-like impurities in the continuum model.
Energy Technology Data Exchange (ETDEWEB)
Kneur, J.L
2006-06-15
This document is divided into 2 parts. The first part describes a particular re-summation technique of perturbative series that can give a non-perturbative results in some cases. We detail some applications in field theory and in condensed matter like the calculation of the effective temperature of Bose-Einstein condensates. The second part deals with the minimal supersymmetric standard model. We present an accurate calculation of the mass spectrum of supersymmetric particles, a calculation of the relic density of supersymmetric black matter, and the constraints that we can infer from models.
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Carneiro, D F; Sampaio, M D; Nemes, M C
2003-01-01
We compute the three loop $\\beta$ function of the Wess-Zumino model to motivate implicit regularization (IR) as a consistent and practical momentum-space framework to study supersymmetric quantum field theories. In this framework which works essentially in the physical dimension of the theory we show that ultraviolet are clearly disantangled from infrared divergences. We obtain consistent results which motivate the method as a good choice to study supersymmetry anomalies in quantum field theories.
F-theory and M-theory perspectives on N=2 supersymmetric gauge theories in four dimensions
Wissanji, Alisha
2012-01-01
Deformations of the original F-theory background are proposed. These lead to multiple new dualities and physical phenomena. We concentrate on one model where we let seven-branes wrap a multi-centered Taub-NUT space instead of R4. This configuration provides a successful F-theory embedding of a class of recently proposed four-dimensional N = 2 superconformal (SCFT) \\`a la Gaiotto. Aspects of Argyres- Seiberg duality, of the new Gaiotto duality, as well as of the branes network of Benini- Benvenuti and Tachikawa are captured by our construction. The supergravity theory for the conformal case is also briefly discussed. Extending our construction to the non-conformal case, we find interesting cascading behavior in four-dimensional gauge theories with N = 2 supersymmetry. Since the analysis of this unexpected phenomenon is quite difficult in the language of type IIB/F-theory, we turn to the type IIA/M-theory description where the origin of the N = 2 cascade is clarified. Using the T-dual type IIA brane language, w...
A supersymmetric grand unified theory of flavour with PSL{sub 2}(7)xSO(10)
Energy Technology Data Exchange (ETDEWEB)
King, Stephen F., E-mail: king@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Luhn, Christoph, E-mail: christoph.luhn@soton.ac.u [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom)
2010-06-11
We construct a realistic Supersymmetric Grand Unified Theory of Flavour based on PSL{sub 2}(7)xSO(10), where the quarks and leptons in the 16 of SO(10) are assigned to the complex triplet representation of PSL{sub 2}(7), while the flavons are assigned to a combination of sextets and anti-triplets of PSL{sub 2}(7). Using a D-term vacuum alignment mechanism, we require the flavon sextets of PSL{sub 2}(7) to be aligned along the 3-3 direction leading to the third family Yukawa couplings, while the flavon anti-triplets describe the remaining Yukawa couplings. Other sextets are aligned along the neutrino flavour symmetry preserving directions leading to tri-bimaximal neutrino mixing via a type II see-saw mechanism, with predictions for neutrinoless double beta decay and cosmology.
Spacetime and flux tube S-matrices at finite coupling for N=4 supersymmetric Yang-Mills theory.
Basso, Benjamin; Sever, Amit; Vieira, Pedro
2013-08-30
We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.
Non-renormalization of the $V\\bar cc$-vertices in ${\\cal N}=1$ supersymmetric theories
Stepanyantz, K V
2016-01-01
Using the Slavnov--Taylor identities we prove that the three-point ghost vertices with a single line of the quantum gauge superfield are not renormalized in all loops in ${\\cal N}=1$ supersymmetric gauge theories. This statement is verified by the explicit one-loop calculation made by the help of the BRST invariant version of the higher covariant derivative regularization. Using the restrictions to the renormalization constants which are imposed by the non-renormalization of the considered vertices we express the exact NSVZ $\\beta$-function in terms of the anomalous dimensions of the Faddeev--Popov ghosts and of the quantum gauge superfield. In the expression for the NSVZ $\\beta$-function obtained in this way the contributions of the Faddeev--Popov ghosts and of the matter superfields have the same structure.
Subtleties in the beta-function calculation of N = 1 supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Cherchiglia, A.L. [ICEx, Universidade Federal de Minas Gerais, Departamento de Fisica, P.O. Box 702, Belo Horizonte, MG (Brazil); Universidad de Granada, Departamento de Fisica Teorica y del Cosmos and CAFPE, Granada (Spain); Sampaio, Marcos [ICEx, Universidade Federal de Minas Gerais, Departamento de Fisica, P.O. Box 702, Belo Horizonte, MG (Brazil); Hiller, B. [CFisUC, Universidade de Coimbra, Departamento de Fisica, Faculdade de Ciencias e Tecnologia, Coimbra (Portugal); Scarpelli, A.P.B. [Setor Tecnico-Cientifico, Departamento de Policia Federal, Sao Paulo (Brazil)
2016-02-15
We investigate some peculiarities in the calculation of the two-loop beta function of N = 1 supersymmetric models which are intimately related to the so-called ''anomaly puzzle''. There is an apparent paradox when the computation is performed in the framework of the covariant derivative background field method. In this formalism, there is obtained a finite two-loop effective action, although a non-null coefficient for the beta function is achieved by means of the renormalized two-point function in the background field. We show that if the standard background field method is used, this two-point function has a divergent part which allows for the calculation of the beta function via the renormalization constants, as usual. Therefore, we conjecture that this paradox has its origin in the covariant supergraph formalism itself, possibly being an artifact of the rescaling anomaly. (orig.)
Renormalization theory and ultraviolet stability for scalar fields via renormalization group methods
Energy Technology Data Exchange (ETDEWEB)
Gallavotti, G.
1985-04-01
A self-contained analysis is given of the simplest quantum fields from the renormalization group point of view: multiscale decomposition, general renormalization theory, resummations of renormalized series via equations of the Callan-Symanzik type, asymptotic freedom, and proof of ultraviolet stability for sine-Gordon fields in two dimensions and for other super-renormalizable scalar fields. Renormalization in four dimensions (Hepp's theorem and the De Calan--Rivasseau nexclamation bound) is presented and applications are made to the Coulomb gases in two dimensions and to the convergence of the planar graph expansions in four-dimensional field theories (t' Hooft--Rivasseau theorem).
Anatomy and phenomenology of flavor and CP violation in supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Altmannshofer, Wolfgang
2010-07-20
The main subject of this PhD thesis is a comprehensive and systematic analysis of flavor and CP violating low energy processes in the framework of the MSSM, the minimal supersymmetric extension of the Standard Model. Supersymmetric (SUSY) models are among the best motivated and most thoroughly analyzed New Physics (NP) models. The new degrees of freedom predicted by Supersymmetry are expected to have masses of the order of the TeV scale and the direct search for these particles is one of the major goals at the LHC. A complementary strategy to probe the MSSM is given by the analysis of low energy high-precision observables, that can be modified through virtual effects of the new degrees of freedom. Of particular importance in this respect are so-called Flavor Changing Neutral Current (FCNC) processes that, forbidden in the Standard Model at the tree level, are highly sensitive probes of the flavor structure of NP models. We first analyze model independently low energy processes that show high sensitivity to the new sources of flavor and CP violation contained in the MSSM. Next, we discuss in detail the rich flavor structure of the MSSM and the implied SUSY contributions to FCNC and CP violating observables both in the low and high tan {beta} regime. In fact, well measured low energy observables lead to remarkably strong constraints on the MSSM parameter space, which is often referred to as the SUSY flavor problem. We outline possibilities to control dangerously large SUSY effects in such observables and analyze the implied predictions for those low energy processes that are not measured with high precision, yet. We consider both the Minimal Flavor Violating MSSM and SUSY models based on abelian and non-abelian flavor symmetries that show representative flavor structures in the soft SUSY breaking terms. We identify the distinctive patterns of SUSY effects in the low energy observables, focussing in particular on CP violation in the b {yields} s{gamma} transition, the
Koehn, Michael
2015-01-01
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are automatically superconducting, leading to important cosmological effects and constraints. We investigate the impact of nontrivial kinetic interactions, present in a number of particle physics models of interest in cosmology, on the relationship between supersymmetry and supercurrents on strings. We find that in some cases it is possible for superconductivity to be disrupted by the extra interactions.
Buchel, Alexander Sergeevich
In the first part of this thesis we study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load. We study this transition at low temperature for small tension. We discuss the appropriate thermodynamic limit of these theories: a large class of boundary conditions is identified for which the energy release for a crack becomes independent of the macroscopic shape of the material. We prove that the energy release in an isotropically stretched material due to the creation of an arbitrary curvy cut is the same to cubic order as the energy release for the straight cut with the same end points. We find the normal modes and the energy spectrum for crack shape fluctuations and for crack surface phonons, under a uniform isotropic tension. For small uniform isotropic tension in two dimensions we calculate the essential singularity associated with fracturing the material in a saddle point approximation including quadratic fluctuations. We calculate the asymptotic ratio of the high-order elastic coefficients of the inverse bulk modulus and argue that the result is unchanged by nonlinearities. In the second part of this thesis we study dualities in supersymmetric field theories. We derive S-dualities in scale invariant N = 2 supersymmetric gauge theories by embedding those theories in asymptotically free theories with higher rank gauge groups. We proceed then to study ``ultrastrong'' coupling points in scale- invariant N = 2 gauge theories. Using the low-energy field theory arguments we relate these theories to other known N = 2 CFT. Finally, we argue that the topology of the quantum coupling space and the low energy effective action on the Coulomb branch of scale invariant N = 2 SU(n) gauge theories pick out a preferred nonperturbative definition of the gauge coupling up to non-singular holomorphic reparameterization
N=2 supersymmetric gauge theory on connected sums of $S^2\\times S^2$
Festuccia, Guido; Winding, Jacob; Zabzine, Maxim
2016-01-01
We construct 4D $\\mathcal{N}=2$ theories on an infinite family of 4D toric manifolds with the topology of connected sums of $S^2 \\times S^2$. These theories are constructed through the dimensional reduction along a non-trivial $U(1)$-fiber of 5D theories on toric Sasaki-Einstein manifolds. We discuss the conditions under which such reductions can be carried out and give a partial classification result of the resulting 4D manifolds. We calculate the partition functions of these 4D theories and they involve both instanton and anti-instanton contributions, thus generalizing Pestun's famous result on $S^4$.
Comparison between experiment and perturbation theory for solitons in Josephson junctions
DEFF Research Database (Denmark)
Pedersen, Niels Falsig; Welner, D.
1984-01-01
Experiments have been made on long inline and overlap Josephson junctions at various temperatures and current densities. The junctions had parameters such that the recently developed perturbation theory for soliton motion according to the modified sine-Gordon equation should be applicable....... A comparison showed that this is the case, and the damping constant was derived as a function of the temperature. In addition, results were obtained for the soliton-antisoliton annihilation process. A fine structure in the zero-field steps at low temperatures is interpreted as being due to plasma oscillations...
Equivalent bosonic theory for the massive Thirring model with non-local interaction
Li, Kang; Naon, Carlos
1997-01-01
We study, through path-integral methods, an extension of the massive Thirring model in which the interaction between currents is non-local. By examining the mass-expansion of the partition function we show that this non-local massive Thirring model is equivalent to a certain non-local extension of the sine-Gordon theory. Thus, we establish a non-local generalization of the famous Coleman's equivalence. We also discuss some possible applications of this result in the context of one-dimensional...
Gudnason, Sven Bjarke; Sasaki, Shin
2015-01-01
Construction of a supersymmetric extension of the Skyrme term was a long-standing problem because of the auxiliary field problem; that is, the auxiliary field may propagate and cannot be eliminated, and the problem of having fourth-order time derivative terms. In this paper, we construct for the first time a supersymmetric extension of the Skyrme term in four spacetime dimensions, in the manifestly supersymmetric superfield formalism that does not suffer from the auxiliary field problem. Chiral symmetry breaking in supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions) but also in the same number of quasi-NG bosons so that the low-energy theory is described by an SL(N,C)-valued matrix field instead of SU(N) for NG bosons. The solution of auxiliary fields is trivial on the canonical branch of the auxiliary field equation, in which case our model results in a fourth-order derivative term that is not the Skyrme term. For the case of SL(2,C), we find explicitly a nontrivial solution to th...
Notes on equivalences and Higgs branches in N=2 supersymmetric Yang-Mills theory
Danielsson, U H; Danielsson, Ulf H; Stjernberg, Par
1996-01-01
In this paper we investigate how various equivalences between effective field theories of N=2 SUSY Yang-Mills theory with matter can be understood through Higgs breaking, i.e. by giving expectation values to squarks. We give explicit expressions for the flat directions for a wide class of examples.
A Twistor Approach to One-Loop Amplitudes in N=1 Supersymmetric Yang-Mills Theory
Bedford, J; Spence, B; Travaglini, G; Bedford, James; Brandhuber, Andreas; Spence, Bill; Travaglini, Gabriele
2004-01-01
We extend the twistor string theory inspired formalism introduced in hep-th/0407214 for calculating loop amplitudes in N=4 super Yang-Mills theory to the case of N=1 (and N=2) super Yang-Mills. Our approach yields a novel representation of the gauge theory amplitudes as dispersion integrals, which are surprisingly simple to evaluate. As an application we calculate one-loop maximally helicity violating (MHV) scattering amplitudes with an arbitrary number of external legs. The result we obtain agrees precisely with the expressions for the N=1 MHV amplitudes derived previously by Bern, Dixon, Dunbar and Kosower using the cut-constructibility approach.
R-parity and The Simplest Supersymmetric Left-Right Theory
Perez, Pavel Fileviez
2008-01-01
We propose a simple renormalizable left-right theory where R-parity is spontaneously broken and neutrino masses are generated through the Type I seesaw mechanism and R-parity violation. In this theory R-parity and the gauge symmetry are broken by the sneutrino vacuum expectation values and there is no Majoron problem. The SU(2)_R and R-parity violation scales are determined by the SUSY breaking scale making the model very predictive. We discuss the spectrum and possible tests of the theory through the neutralinos, charginos, Z' and W_R decays at the Large Hadron Collider.
Bern, Z; Dixon, L J; Kosower, D A; Smirnov, V A; Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-01-01
We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around e=0, and obtain analytic expressions for the poles from 1/e^8 through 1/e^4. We give numerical results for the coefficients of the 1/e^3 and 1/e^2 poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/e^2 coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing zeta_3^2, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimat...
String Corrections to the Holographic RG Flow of Supersymmetric SU(N+M) x SU(N) Gauge Theory
Frolov, S; Tseytlin, Arkady A; Frolov, Sergey; Klebanov, Igor R.; Tseytlin, Arkady A.
2002-01-01
We study leading string corrections to the type IIB supergravity solution dual to the ${\\cal N}=1$ supersymmetric $SU(N+M)\\times SU(N)$ gauge theory coupled to bifundamental chiral superfields $A_i, B_j$, $i,j=1,2$. This solution was found in hep-th/0007191, and its asymptotic form describing logarithmic RG flow was constructed in hep-th/0002159. The leading tree-level string correction to the type IIB string effective action is represented by the invariant of the form $\\alpha'^3 (R^4 + ...)$. Since the background contains 3-form field strengths, we need to know parts of this invariant that depend on them. By analyzing the 5-point superstring scattering amplitudes we show that only a few specific $R^3 (H_3)^2$ and $R^3 (F_3)^2$ terms are present in the effective action. Their contribution to the holographic RG flow turns out to be of the same order as of the $R^4$ terms. This fact is crucial for finding agreement between the $\\alpha'$-corrected radial dependence of the supergravity fields and the RG flow dict...
Bourjaily, Jacob L.; Heslop, Paul; Tran, Vuong-Viet
2016-05-01
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.
Bourjaily, Jacob L; Heslop, Paul; Tran, Vuong-Viet
2016-05-13
We use the soft-collinear bootstrap to construct the 8-loop integrand for the 4-point amplitude and 4-stress-tensor correlation function in planar maximally supersymmetric Yang-Mills theory. Both have a unique representation in terms of planar, conformal integrands grouped according to a hidden symmetry discovered for correlation functions. The answer we find exposes a fundamental tension between manifest locality and planarity with manifest conformality not seen at lower loops. For the first time, the integrand must include terms that are finite even on-shell and terms that are divergent even off-shell (so-called pseudoconformal integrals). We describe these novelties and their consequences in this Letter, and we make the full correlator and amplitude available as part of the Supplemental Material.
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
Supersymmetric extended string field theory in NSn sector and NSn−1–R sector
Directory of Open Access Journals (Sweden)
Masako Asano
2016-09-01
Full Text Available We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu–Schwarz (NS sectors with or without one Ramond (R sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [1]. The theory for NSn sector and NSn−1–R sector contains general n-th rank tensor fields and (n−1-th rank spinor–tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor–tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.
Supersymmetric extended string field theory in NSn sector and NSn - 1-R sector
Asano, Masako; Kato, Mitsuhiro
2016-09-01
We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu-Schwarz (NS) sectors with or without one Ramond (R) sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [1]. The theory for NSn sector and NS n - 1-R sector contains general n-th rank tensor fields and (n - 1)-th rank spinor-tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor-tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-10-01
We point out that the non-critical version of the k-fractional superstring theory can be described by k-cut critical points of the matrix models. In particular, in comparison with the spectrum structure of fractional super-Liouville theory, we show that (p,q) minimal fractional superstring theories appear in the Z-symmetry breaking critical points of the k-cut two-matrix models and the operator contents and string susceptibility coincide on both sides. By using this correspondence, we also propose a set of primary operators of the fractional superconformal ghost system which consistently produces the correct gravitational scaling critical exponents of the on-shell vertex operators.
Exact Slope and Interpolating Functions in N=6 Supersymmetric Chern-Simons Theory
Gromov, Nikolay; Sizov, Grigory
2014-09-01
Using the quantum spectral curve approach we compute, exactly, an observable (called slope function) in the planar Aharony-Bergman-Jafferis-Maldacena theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization based calculation for a similar observable in Marino and Putrov [J. High Energy Phys. 06 (2010) 011], we conjecture an exact expression for h(λ).
Evidence for discrete chiral symmetry breaking in $N = 1$ supersymmetric Yang-Mills theory
Kirchner, R; Montvay, István; Spanderen, K; Westphalen, J
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking $Z_4 \\to Z_2$ caused by gaugino condensation.
Evidence for discrete chiral symmetry breaking in N=1 supersymmetric Yang-Mills theory
Desy-Münster Collaboration; Kirchner, R.; Montvay, I.; Westphalen, J.; Luckmann, S.; Spanderen, K.
1999-01-01
In a numerical Monte Carlo simulation of SU(2) Yang-Mills theory with dynamical gauginos we find evidence for two degenerate ground states at the supersymmetry point corresponding to zero gaugino mass. This is consistent with the expected pattern of spontaneous discrete chiral symmetry breaking Z4-->Z2 caused by gaugino condensation.
Energy Technology Data Exchange (ETDEWEB)
Bern, Zvi; Czakon, Michael; Dixon, Lance J.; Kosower, David A.; Smirnov, Vladimir A.
2006-11-15
We present an expression for the leading-color (planar) four-loop four-point amplitude of N = 4 supersymmetric Yang-Mills theory in 4-2{epsilon} dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around {epsilon} = 0, and obtain analytic expressions for the poles from 1/{epsilon}{sup 8} through 1/{epsilon}{sup 4}. We give numerical results for the coefficients of the 1/{epsilon}{sup 3} and 1/e{sup 2} poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/{epsilon}{sup 2} coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing {zeta}{sub 3}{sup 2}, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.
Fractional supersymmetric Liouville theory and the multi-cut matrix models
Irie, Hirotaka
2009-01-01
We argue that the non-critical version of the k-fractional superstring theory can be described with the k-cut critical points of the matrix models. In particular we show that, from the spectrum structure of fractional super-Liouville theory, (p,q) minimal fractional superstrings live in the Z_k-symmetry breaking critical points of the k-cut two-matrix models, and that the operator contents and string susceptibility coincide in both sides. By using this correspondence, we also propose the set of primary operators of the fractional superconformal ghost system which consistently gives the correct gravitational scaling critical exponents of the on-shell vertex operators.
Non-Supersymmetric Theories with Light Scalar Fields and Large Hierarchies
Strassler, M J
2003-01-01
Various nonsupersymmetric theories at large but finite $N$ are argued to permit light scalars and large hierarchies without fine-tuning. In a dual string description, the hierarchy results from competition between classical and quantum effects. In some cases the flow may end when a string mode becomes tachyonic and condenses, thereby realizing a quantum-mechanically stable Randall-Sundrum hierarchy scenario. Among possible applications, it is suggested that lattice simulation of \
Local existence of N=1 supersymmetric gauge theory in four Dimensions
Energy Technology Data Exchange (ETDEWEB)
Akbar, Fiki T. [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung Jl. Ganesha no. 10 Bandung, 40132 (Indonesia); Gunara, Bobby E.; Zen, Freddy P.; Triyanta [Theoretical Physics Laboratory, Theoretical High Energy Physics and Instrumentation Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung Jl. Ganesha no. 10 Bandung, 40132 (Indonesia); Indonesian Center of Theoretical and Mathematical Physics (ICTMP) (Indonesia)
2015-04-16
In this paper, we shall prove the local existence of N=1 supersymmetry gauge theory in 4 dimension. We start from the Lagrangian for coupling chiral and vector multiplets with constant gauge kinetic function and only considering a bosonic part by setting all fermionic field to be zero at level equation of motion. We consider a U(n) model as isometry for scalar field internal geometry. And we use a nonlinear semigroup method to prove the local existence.
Lepton-Flavour Violation in Ordinary and Supersymmetric Grand Unified Theories
Lim, C S; Taga, Bungo
2000-01-01
By an explicit calculation we show that in ordinary SU(5) logarithmic divergence in the amplitude of $\\mu \\to e\\gamma$ cancels among diagrams and remaining finite part is suppressed by at least $1/M_{GUT}^2$. In SUSY SU(5), when the effect of flavour changing wave function renormalization is taken into account such logarithmic correction disappears, provided a condition is met among SUSY breaking masses. In SUGRA-inspired SUSY GUT the remaining logarithmic effect is argued not to be taken as a prediction of the theory.
A $\\mathcal{N}=2$ Supersymmetric $AdS_4$ Solution in M-theory
Lozano, Yolanda; Montero, Jesús
2015-01-01
We find a new $\\mathcal{N}=2$ $AdS_4$ solution in M-theory supported by purely magnetic flux via a sequence of abelian and non-abelian T-dualities. This provides the second known example in this class besides the uplift of the Pernici and Sezgin solution to 7d gauged supergravity constructed in the eighties. We compute the free energy of the solution, and show that it scales as $N^{3/2}$. It is intriguing that even though the natural holographic interpretation is in terms of M5-branes wrapped on a special Lagrangian 3-cycle, this solution does not exhibit the expected $N^3$ behavior.
Supersymmetric SO(N) from a Planck-scale statistical theory
Allen, Roland E
2010-01-01
Several refinements are made in a theory which starts with a Planck-scale statistical picture and ends with supersymmetry and a coupling of fundamental fermions and bosons to SO(N) gauge fields. In particular, more satisfactory treatments are given for (1) the transformation from the initial Euclidean form of the path integral for fermionic fields to the usual Lorentzian form, (2) the corresponding transformation for bosonic fields (which is much less straightforward), (3) the transformation from an initial primitive supersymmetry to the final standard form (containing, e.g., scalar sfermions and their auxiliary fields), (4) the initial statistical picture, and (5) the transformation to an action which is invariant under general coordinate transformations.
Dynamical Supersymmetry Breaking versus Run-away behavior in Supersymmetric Gauge Theories
Shirman, Yu
1996-01-01
We consider Dynamical Supersymmetry Breaking (DSB) in models with classical flat directions. We analyze a number of examples, and develop a systematic approach to determine if classical flat directions are stabilized in the full quantum theory, or lead to run-away behavior. In some cases pseudo-flat directions remain even at the quantum level before taking into account corrections to the Kähler potential. We show that in certain limits these corrections are calculable. In particular, we find that in the Intriligator-Thomas $SU(2)$ and its generalizations, a potential for moduli is generated. Moreover, there is a region of the parameter space where Kähler potential corrections lead to calculable (local) minima at large but finite distance from the origin.
Anagnostopoulos, Konstantinos N; Nishimura, Jun
2012-01-01
The IKKT or IIB matrix model has been postulated to be a non perturbative definition of superstring theory. It has the attractive feature that spacetime is dynamically generated, which makes possible the scenario of dynamical compactification of extra dimensions, which in the Euclidean model manifests by spontaneously breaking the SO(10) rotational invariance (SSB). In this work we study using Monte Carlo simulations the 6 dimensional version of the Euclidean IIB matrix model. Simulations are found to be plagued by a strong complex action problem and the factorization method is used for effective sampling and computing expectation values of the extent of spacetime in various dimensions. Our results are consistent with calculations using the Gaussian Expansion method which predict SSB to SO(3) symmetric vacua, a finite universal extent of the compactified dimensions and finite spacetime volume.
Lü, H; Stelle, Kellogg S
2006-01-01
The notion of {\\it generalised structure groups} and {\\it generalised holonomy groups} has been introduced in supergravity, in order to discuss the spinor rotations generated by commutators of supercovariant derivatives when non-vanishing form fields are included, with their associated gamma-matrix structures that go beyond the usual \\Gamma_{MN} of the Riemannian connection. In this paper we investigate the generalisations to the usual Riemannian structure and holonomy groups that result from the inclusion of higher-order string or M-theory corrections in the supercovariant derivative. Even in the absence of background form fields, these corrections introduce additional terms \\Gamma_{M_1... M_6} in the supercovariant connection, and hence they lead to enlarged structure and holonomy groups. In some cases, the corrected equations of motion force form fields to become non-zero too, which can further enlarge the groups. Our investigation focuses on the generalised structure and holonomy groups in the transverse ...
Nonlinear Dynamics of Globally Coupled Sine-Gordon Equations
2011-05-01
studied too, including a triangular configuration of linearly coupled parallel fiber Bragg gratings [15], coupled triplets of Gross-Pitaevskii...B. Dueholm, O. A. Levring, J. Mygind, N. F. Pedersen , O. H. Soerensen, and M. Cirillo, Phys. Rev. Lett. 46, 1299 (1981); E. Joergensen, V. P...Malomed, Phys. Rev. B 37, 9325 (1988); A. V. Ustinov, H. Kohlstedt, M. Cirillo, N. F. Pedersen , G. Hallmanns, and C. Heiden, ibid. B 48, 10614
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
Bern, Z; Kosower, D A; Roiban, R; Spradlin, M; Vergu, C; Volovich, A
2008-01-01
We give a representation of the parity-even part of the planar two-loop six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of loop-momentum integrals with simple dual conformal properties. We evaluate the integrals numerically in order to test directly the ABDK/BDS all-loop ansatz for planar MHV amplitudes. We find that the ansatz requires an additive remainder function, in accord with previous indications from strong-coupling and Regge limits. The planar six-gluon amplitude can also be compared with the hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in arXiv:0803.1466 [hep-th]. After accounting for differing singularities and other constants independent of the kinematics, we find that the Wilson loop and MHV-amplitude remainders are identical, to within our numerical precision. This result provides non-trivial confirmation of a proposed n-point equivalence between Wilson loops and planar MHV amplitudes, and suggests that an additional mechanism besides dual conformal...
Nearly Supersymmetric Dark Atoms
Energy Technology Data Exchange (ETDEWEB)
Behbahani, Siavosh R.; Jankowiak, Martin; /SLAC /Stanford U., ITP; Rube, Tomas; /Stanford U., ITP; Wacker, Jay G.; /SLAC /Stanford U., ITP
2011-08-12
Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed and several benchmark models are described. General features of non-relativistic supersymmetric bound states are emphasized.
Proton Decay in Minimal Supersymmetric SU(5)
Bajc, Borut; Perez, Pavel Fileviez; Senjanovic, Goran
2002-01-01
We systematically study proton decay in the minimal supersymmetric SU(5) grand unified theory. We find that although the available parameter space of soft masses and mixings is quite constrained, the theory is still in accord with experiment.
Instanton Corrected Non-Supersymmetric Attractors
Dominic, Pramod
2010-01-01
We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.
The holographic supersymmetric Casimir energy
Benetti Genolini, Pietro; Cassani, Davide; Martelli, Dario; Sparks, James
2017-01-01
We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, which are dual to superconformal field theories on curved backgrounds S1×M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S1×R4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory supersymmetric relation between charges.
Supersymmetric R4-actions in ten dimensions
Roo, M. de; Suelmann, H.; Wiedemann, A.
1992-01-01
We construct supersymmetric R+R4-actions in ten dimensions. Two invariants, of which the bosonic parts are known from string amplitude and sigma model calculations, are obtained. One of these invariants can be generalized to an R+F2+F4-invariant for supersymmetric Yang-Mills theory coupled to superg
Energy Technology Data Exchange (ETDEWEB)
Sandbrink, Dirk
2015-01-26
One of the most promising candidates to describe the physics beyond the standard model is the so-called supersymmetry. This work was created in the context of the DESY-Muenster-Collaboration, which studies in particular the N=1 supersymmetric Yang-Mills theory (SYM). SYM is a comparatively simple theory, which is therefore well-suited to study the expected properties of a supersymmetric theory with the help of Monte Carlo simulations on the lattice. This thesis is focused on the numerical determination of the quarkpotential, the glueball masses and the phase structur of the N=1 supersymmetric Yang-Mills theory. The quarkpotential is used to calculate the Sommer scale, which in turn is needed to convert the dimensionless lattice spacing into physical units. Glueballs are hypothetical particles built out of gluons, their masses are relatively hard to determine in lattice simulations due to their pure gluonic nature. For this reason, various methods are studied to reduce the uncertainties of the mass determination. The focus lies on smearing methods and their use in variational smearing as well as on the use of different glueball operators. Lastly, a first look is taken at the phase diagram of the model at finite temperature. Various simulations have been performed at finite temperature in parallel to those performed at temperature zero to analyse the behaviour of the Polyakov loop and the gluino condensate in greater detail.
Harnik, R
2004-01-01
Supersymmetric models have traditionally been assumed to be perturbative up to high scales due to the requirement of calculable unification. In this note I review the recently proposed `Fat Higgs' model which relaxes the requirement of perturbativity. In this framework, an NMSSM-like trilinear coupling becomes strong at some intermediate scale. The NMSSM Higgses are meson composites of an asymptotically-free gauge theory. This allows us to raise the mass of the Higgs, thus alleviating the MSSM of its fine tuning problem. Despite the strong coupling at an intermediate scale, the UV completion allows us to maintain gauge coupling unification.
Ilinskii, K N; Melezhik, V S; Ilinski, K N; Kalinin, G V; Melezhik, V V
1994-01-01
We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.
Konishi, K I
2000-01-01
Several distinct mechanisms of confinement and dynamical symmetry breaking (DSB) are identified, in a class of supersymmetric $SU(n_c)$, $USp(2n_c)$ and $SO(n_c)$ gauge theories. In some of the vacua, the magnetic monopoles carrying nontrivial flavor quantum numbers condense, causing confinement and symmetry breaking simultaneously. In more general classes of vacua, however, the effective low-energy degrees of freedom are found to be constituents of the monopoles - dual (magnetic) quarks. These magnetic quarks condense and give rise to confinement and DSB. We find two more important classes of vacua, one is in various universality classes of nontrivial superconformal theories (SCFT), another in free-magnetic phase.
The supersymmetric flavor problem
Dimopoulos, Savas K; Dimopoulos, Savas; Sutter, Dave
1995-01-01
The supersymmetric SU(3)\\times SU(2)\\times U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes \\mu \\rightarrow e + \\gamma and K^0 - \\bar{K}^0 mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for \\mu \\rightarrow e + \\gamma exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than M_{\\rm Planck}.
Supersymmetric vacua in random supergravity
Bachlechner, Thomas C.; Marsh, David; McAllister, Liam; Wrase, Timm
2013-01-01
We determine the spectrum of scalar masses in a supersymmetric vacuum of a general mathcal{N}=1 supergravity theory, with the Kähler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P=exp left( {{{{-2{N^2}{{{left| W right|}}^2}}} left/ {{m_{susy}^2}} right.}} right) , with W denoting the superpotential and m susy the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N ≫ 1. We conclude that for left| W right|gtrsim {{{{m_{susy}}}} left/ {N} right.} , tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Supersymmetric counterterms from new minimal supergravity
Assel, Benjamin; Martelli, Dario
2014-01-01
We present a systematic classification of counterterms of four-dimensional supersymmetric field theories on curved space, obtained as the rigid limit of new minimal supergravity. These are supergravity invariants constructed using the field theory background fields. We demonstrate that if the background preserves two supercharges of opposite chirality, then all dimensionless counterterms vanish. This implies that a supersymmetric renormalisation scheme is free of ambiguities. When only one Euclidean supercharge is preserved, we describe the ambiguities that appear in supersymmetric observables, in particular in the dependence on marginal couplings.
Quantum integrability and supersymmetric vacua
Nekrasov, Nikita A.; Shatashvili, Samson L.
2009-01-01
This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail. We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to ...
Supersymmetric Adler Functions and Holography
Iwanaga, Masaya; Sakai, Tadakatsu
2016-01-01
We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.
Giant magnons of string theory in the lambda background
Appadu, Calan; Hollowood, Timothy J.; Miramontes, J. Luis; Price, Dafydd; Schmidtt, David M.
2017-07-01
The analogues of giant magnon configurations are studied on the string world sheet in the lambda background. This is a discrete deformation of the AdS5× S 5 background that preserves the integrability of the world sheet theory. Giant magnon solutions are generated using the dressing method and their dispersion relation is found. This reduces to the usual dyonic giant magnon dispersion relation in the appropriate limit and becomes relativistic in another limit where the lambda model becomes the generalized sine-Gordon theory of the Pohlmeyer reduction. The scattering of giant magnons is then shown in the semi-classical limit to be described by the quantum S-matrix that is a quantum group deformation of the conventional giant magnon S-matrix. It is further shown that in the small g limit, a sector of the S-matrix is related to the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.
Supersymmetric Vacua in Random Supergravity
Bachlechner, Thomas C; McAllister, Liam; Wrase, Timm
2012-01-01
We determine the spectrum of scalar masses in a supersymmetric vacuum of a general N=1 supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P = exp(-2N^2|W|^2/m_{susy}^2), with W denoting the superpotential and m_{susy} the supersymmetric mass scale; for more general distributions of the...
New topological structures of Skyrme theory: baryon number and monopole number
Energy Technology Data Exchange (ETDEWEB)
Cho, Y.M. [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China); Konkuk University, Seoul (Korea, Republic of); Seoul National University, School of Physics and Astronomy, Seoul (Korea, Republic of); Kimm, Kyoungtae [Seoul National University, Faculty of Liberal Education, Seoul (Korea, Republic of); Yoon, J.H. [Konkuk University, Department of Physics, Seoul (Korea, Republic of); Zhang, Pengming [Chinese Academy of Science, Institute of Modern Physics, Lanzhou (China)
2017-02-15
Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology π{sub 3}(S{sup 3}) and the monopole topology π{sub 2}(S{sup 2}). With this we propose to classify the skyrmions by two topological numbers (m, n), the monopole number m and the shell (radial) number n. In this scheme the popular (non spherically symmetric) skyrmions are classified as the (m, 1) skyrmions but the spherically symmetric skyrmions are classified as the (1, n) skyrmions, and the baryon number B is given by B = mn. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers (p, q). This puts the Skyrme theory in a totally new perspective. (orig.)
On the uniqueness of supersymmetric attractors
Directory of Open Access Journals (Sweden)
Taniya Mandal
2015-10-01
Full Text Available In this paper we discuss the uniqueness of supersymmetric attractors in four-dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.
Supersymmetric Spacetimes from Curved Superspace
Kuzenko, Sergei M
2015-01-01
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitra...
Supersymmetric Displaced Number States
Directory of Open Access Journals (Sweden)
Fredy R. Zypman
2015-06-01
Full Text Available We introduce, generate and study a family of supersymmetric displaced number states (SDNS that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.
Choi, Gongjun
2015-01-01
We study asymptotically free SU($N_c$) gauge theories with ${\\cal N}=1$ supersymmetry, including the purely gluonic theory and theories with $N_f$ copies of a pair of massless chiral superfields in the respective representations $R$ and $\\bar R$ of SU($N_c$). The cases in which $R$ is the fundamental representation and the symmetric and antisymmetric rank-2 tensor representation are considered. We calculate Pad\\'e approximants to the beta functions for these theories in the $\\overline{\\rm DR}$ scheme up to four-loop order for the gluonic theory and up to three-loop order for the theories with matter superfields and compare results for IR zeros and poles with results from the NSVZ beta function. Our calculations provide a quantitative measure, for these theories, of how well finite-order perturbative results calculated in one scheme reproduce properties of a known beta function calculated in a different scheme.
The Minimal Supersymmetric Fat Higgs Model
Harnik, R; Larson, D T; Murayama, H; Harnik, Roni; Kribs, Graham D.; Larson, Daniel T.; Murayama, Hitoshi
2003-01-01
We present a calculable supersymmetric theory of a composite ``fat'' Higgs boson. Electroweak symmetry is broken dynamically through a new gauge interaction that becomes strong at an intermediate scale. The Higgs mass can easily be 200-450 GeV along with the superpartner masses, solving the supersymmetric little hierarchy problem. We explicitly verify that the model is consistent with precision electroweak data without fine-tuning. Gauge coupling unification can be maintained despite the inherently strong dynamics involved in electroweak symmetry breaking. Supersymmetrizing the Standard Model therefore does not imply a light Higgs mass, contrary to the lore in the literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum that is distinctly different from the Minimal Supersymmetric Standard Model.
Patterns of flavor signals in supersymmetric models
Energy Technology Data Exchange (ETDEWEB)
Goto, T. [KEK National High Energy Physics, Tsukuba (Japan)]|[Kyoto Univ. (Japan). YITP; Okada, Y. [KEK National High Energy Physics, Tsukuba (Japan)]|[Graduate Univ. for Advanced Studies, Tsukuba (Japan). Dept. of Particle and Nucelar Physics; Shindou, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[International School for Advanced Studies, Trieste (Italy); Tanaka, M. [Osaka Univ., Toyonaka (Japan). Dept. of Physics
2007-11-15
Quark and lepton flavor signals are studied in four supersymmetric models, namely the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate b{yields}s(d) transition observables in B{sub d} and B{sub s} decays, taking the constraint from the B{sub s}- anti B{sub s} mixing recently observed at Tevatron into account. We also calculate lepton flavor violating processes {mu} {yields} e{gamma}, {tau} {yields} {mu}{gamma} and {tau} {yields} e{gamma} for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb and a future Super B Factory. (orig.)
N=2 supersymmetric dynamics for pedestrians
Tachikawa, Yuji
2015-01-01
Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides r...
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.
Supersymmetric non conservative systems
Martínez-Pérez, N E
2015-01-01
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given in the superfield formalism. The corresponding Noether theorem is formulated. As expected, like the energy, the supersymmetric charges are not conserved. Examples are discussed.
Supersymmetric Higgs Bosons and Beyond
Energy Technology Data Exchange (ETDEWEB)
Carena, Marcela; /Fermilab /Chicago U., EFI; Kong, Kyoungchul; /Fermilab /SLAC; Ponton, Eduardo; /Columbia U.; Zurita, Jose; /Fermilab /Buenos Aires U.
2010-08-26
We consider supersymmetric models that include particles beyond the Minimal Supersymmetric Standard Model (MSSM) with masses in the TeV range, and that couple significantly to the MSSM Higgs sector. We perform a model-independent analysis of the spectrum and couplings of the MSSM Higgs fields, based on an effective theory of the MSSM degrees of freedom. The tree-level mass of the lightest CP-even state can easily be above the LEP bound of 114 GeV, thus allowing for a relatively light spectrum of superpartners, restricted only by direct searches. The Higgs spectrum and couplings can be significantly modified compared to the MSSM ones, often allowing for interesting new decay modes. We also observe that the gluon fusion production cross section of the SM-like Higgs can be enhanced with respect to both the Standard Model and the MSSM.
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Fu, Wenbo; Maldacena, Juan; Sachdev, Subir
2016-01-01
We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we disc...
Dynamics of ${\\cal N}=4$ supersymmetric field theories in 2+1 dimensions and their gravity dual
Cottrell, William; Hashimoto, Akikazu
2015-01-01
In this note we consider ${\\cal N}=4$ SYM theories in 2+1 dimensions with gauge group $U(N)\\times U(M)$ and $k$ hypermultiplets charged under the $U(N)$. When $k > 2(N-M)$, the theory flows to a superconformal fixed point in the IR. Theories with $k <2(N-M)$, on the other hand, flows to strong coupling. We explore these theories from the perspective of gravity dual. We find that the gravity duals of theories with $k < (N-M)$ contain enhancons even in situations where repulson singularities are absent. We argue that supergravity description is unreliable in the region near these enhancon points. Instead, we show how to construct reliable sugra duals to particular points on the Coulomb branch where the enhancon is screened. We explore how these singularities reappear as one moves around in Coulomb branch and comment on possible field theory interpretation of this phenomenon. In analyzing gauge/gravity duality for these models, we encountered one unexpected surprise, that the condition for the supergravity...
Electroweak breaking in supersymmetric models
Ibáñez, L E
1992-01-01
We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)
The holographic supersymmetric Casimir energy
Genolini, Pietro Benetti; Martelli, Dario; Sparks, James
2016-01-01
We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.
Supersymmetric defect models and mirror symmetry
Energy Technology Data Exchange (ETDEWEB)
Hook, Anson; Kachru, Shamit; Torroba, Gonzalo
2013-11-01
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d NN = 4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d NN = 2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of NN = 4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.
Supersymmetric Defect Models and Mirror Symmetry
Hook, Anson; Torroba, Gonzalo
2013-01-01
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d N=4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d N=2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of N=4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.
Supersymmetric extended string field theory in NS^n sector and NS^{n-1}-R sector
Asano, Masako
2016-01-01
We construct a class of quadratic gauge invariant actions for extended string fields defined on the tensor product of open superstring state space for multiple open string Neveu-Schwarz (NS) sectors with or without one Ramond (R) sector. The basic idea is the same as for the bosonic extended string field theory developed by the authors [arXiv:1309.3850]. The theory for NS^n sector and NS^{n-1}-R sector contains general n-th rank tensor fields and (n-1)-th rank spinor-tensor fields in the massless spectrum respectively. In principle, consistent gauge invariant actions for any generic type of 10-dimensional massive or massless tensor or spinor-tensor fields can be extracted from the theory. We discuss some simple examples of bosonic and fermionic massless actions.
Non-renormalization theorems andN=2 supersymmetric backgrounds
Energy Technology Data Exchange (ETDEWEB)
Butter, Daniel [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Wit, Bernard de [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Institute for Theoretical Physics, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Lodato, Ivano [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands)
2014-03-28
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Non-renormalization theorems and N=2 supersymmetric backgrounds
Butter, Daniel; Lodato, Ivano
2014-01-01
The conditions for fully supersymmetric backgrounds of general N=2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Nonlocal String Theories on AdS{sub 3} x S{sup 3} and Stable Non-Supersymmetric Backgrounds
Energy Technology Data Exchange (ETDEWEB)
Silverstein, Eva M
2002-01-16
We exhibit a simple class of exactly marginal ''double-trace'' deformations of two dimensional CFTs which have AdS{sub 3} duals, in which the deformation is given by a product of left and right-moving U(1) currents. In this special case the deformation on AdS{sub 3} is generated by a local boundary term in three dimensions, which changes the physics also in the bulk via bulk-boundary propagators. However, the deformation is non-local in six dimensions and on the string worldsheet, like generic non-local string theories (NLSTs). Due to the simplicity of the deformation we can explicitly make computations in the non-local string theory and compare them to CFT computations, and we obtain precise agreement. We discuss the effect of the deformation on closed strings and on D-branes. The examples we analyze include a supersymmetry-breaking but exactly marginal ''double-trace'' deformation, which is dual to a string theory in which no destabilizing tadpoles are generated for moduli nonperturbatively in all couplings, despite the absence of supersymmetry. We explain how this cancellation works on the gravity side in string perturbation theory, and also non-perturbatively at leading order in the deformation parameter. We also discuss possible flat space limits of our construction.
Renormalizability of Supersymmetric Group Field Cosmology
Upadhyay, Sudhaker
2014-01-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Renormalizability of supersymmetric group field cosmology
Upadhyay, Sudhaker
2014-03-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
The Supersymmetric Standard Model
Fayet, Pierre
2016-10-01
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a neutralino, is expected to be stable and a possible candidate for dark matter. The electroweak breaking requires two doublets, leading to several charged and neutral Brout-Englert-Higgs bosons. This also leads to gauge/Higgs unification by providing extra spin-0 partners for the spin-1 W± and Z. It offers the possibility to view, up to a mixing angle, the new 125 GeV boson as the spin-0 partner of the Z under two supersymmetry transformations, i.e. as a Z that would be deprived of its spin. Supersymmetry then relates two existing particles of different spins, in spite of their different gauge symmetry properties, through supersymmetry transformations acting on physical fields in a non-polynomial way. We also discuss how the compactification of extra dimensions, relying on R-parity and other discrete symmetries, may determine both the supersymmetrybreaking and grand-unification scales.
The Supersymmetric Standard Model
Fayet, Pierre
2016-01-01
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a neutralino, is expected to be stable and a possible candidate for dark matter. The electroweak breaking requires two doublets, leading to several charged and neutral Brout- Englert-Higgs bosons. This also leads to gauge/Higgs unification by providing extra spin-0 partners for the spin-1 W$^\\pm$ and Z. It offers the possibility to view, up to a mixing angle, the new 125 GeV boson as the spin-0 partner of the Z under two supersymmetry transformations, i.e. as a Z that would be deprived of its spin. Supersymmetry then relates two existing particles of different spins, in spite of their different gauge symmetry properties, through supersymmetry transformations acting on physical fields in a non-polynomial way. We also discuss how the compactification of extra dimensions, relying ...
A Maximally Supersymmetric Kondo Model
Energy Technology Data Exchange (ETDEWEB)
Harrison, Sarah; Kachru, Shamit; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2012-02-17
We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N = 4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N = 4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial S3 in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.
Spectral properties in supersymmetric matrix models
Energy Technology Data Exchange (ETDEWEB)
Boulton, Lyonell, E-mail: L.Boulton@hw.ac.uk [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Garcia del Moral, Maria Pilar, E-mail: garciamormaria@uniovi.es [Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain); Restuccia, Alvaro, E-mail: arestu@usb.ve [Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas (Venezuela, Bolivarian Republic of); Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain)
2012-03-21
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.
Energy Technology Data Exchange (ETDEWEB)
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.
Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry
Matsui, Chihiro
2016-01-01
We study spinon excitations of the integrable spin-1 (Fateev-Zamolodchikov; FZ) chain and their relation to the hidden supersymmetry. Using the notion of the supercharges earlier introduced to the spin chains, which change the system length by one, we found that they nontrivially act on one of two kinds of the degrees of freedom for the FZ chain. Their actions were obtained to be the same as those of the supercharges defined on the supersymmetric sine-Gordon model, the low-energy effective field theory of the FZ chain. Moreover, we construct the eigenstates which are invariant under the supersymmetric Hamiltonian given as the anti-commutator of the supercharges.
The renormalization group and two dimensional multicritical effective scalar field theory
Morris, T R
1995-01-01
Direct verification of the existence of an infinite set of multicritical non-perturbative FPs (Fixed Points) for a single scalar field in two dimensions, is in practice well outside the capabilities of the present standard approximate non-perturbative methods. We apply a derivative expansion of the exact RG (Renormalization Group) equations in a form which allows the corresponding FP equations to appear as non-linear eigenvalue equations for the anomalous scaling dimension \\eta. At zeroth order, only continuum limits based on critical sine-Gordon models, are accessible. At second order in derivatives, we perform a general search over all \\eta\\ge.02, finding the expected first ten FPs, and {\\sl only} these. For each of these we verify the correct relevant qualitative behaviour, and compute critical exponents, and the dimensions of up to the first ten lowest dimension operators. Depending on the quantity, our lowest order approximate description agrees with CFT (Conformal Field Theory) with an accuracy between ...
Bhattacharya, Subhaditya
2009-01-01
We derive the non-universal gaugino mass ratios in a supergravity (SUGRA) framework where the higgs superfields belong to the non-singlet representations {\\bf 54} and {\\bf 770} in a SO(10) Grand Unified Theory (GUT). We evaluate the ratios for two intermediate breaking chains, namely, $SU(2) \\times SO(7)$ and $SU(4)_C \\times SU(2)_L \\times SU(2)_R (G_{224})$ assuming the breaking of the SO(10) GUT group to the intermediate gauge group and that to the Standard Model (SM) takes place at the GUT scale itself. After a full calculation of the gaugino mass ratios, correcting some mistakes in the earlier calculation for 54, we obtain some new interesting low scale phenomenology of such breaking patterns after running down by the renormalization group equations (RGE). We also study the collider signatures in multilepton channels at the Large Hadron Collider (LHC) experiment for some selected benchmark points allowed by the cold dark matter relic density constraint provided by the WMAP data.
Supersymmetric classical cosmology
Escamilla-Rivera, Celia; Urena-Lopez, L Arturo
2010-01-01
In this work a supersymmetric cosmological model is analyzed in which we consider a general superfield action of a homogeneous scalar field supermultiplet interacting with the scale factor in a supersymmetric FRW model. There appear fermionic superpartners associated with both the scale factor and the scalar field, and classical equations of motion are obtained from the super-Wheeler-DeWitt equation through the usual WKB method. The resulting supersymmetric Einstein-Klein-Gordon equations contain extra radiation and stiff matter terms, and we study their solutions in flat space for different scalar field potentials. The solutions are compared to the standard case, in particular those corresponding to the exponential potential, and their implications for the dynamics of the early Universe are discussed in turn.
The Supersymmetric Particle Spectrum
Barger, V; Ohmann, P
1994-01-01
We examine the spectrum of supersymmetric particles predicted by grand unified theoretical (GUT) models where the electroweak symmetry breaking is accomplished radiatively. We evolve the soft supersymmetry breaking parameters according to the renormalization group equations (RGE). The minimization of the Higgs potential is conveniently described by means of tadpole diagrams. We present complete one-loop expressions for these minimization conditions, including contributions from the matter and the gauge sectors. We concentrate on the low $\\tan \\beta$ fixed point region (that provides a natural explanation of a large top quark mass) for which we find solutions to the RGE satisfying both experimental bounds and fine-tuning criteria. We also find that the constraint from the consideration of the lightest supersymmetric particle as the dark matter of the universe is accommodated in much of parameter space where the lightest neutralino is predominantly gaugino. The supersymmetric mass spectrum displays correlations...
Planarizable Supersymmetric Quantum Toboggans
Directory of Open Access Journals (Sweden)
Miloslav Znojil
2011-02-01
Full Text Available In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate x giving the so called quantum toboggan models (QTM. The consistent theoretical background of this recipe is briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional and reducible to doublets of non-singular ordinary differential equations a.k.a. Sturm-Schrödinger equations containing a weighted energy E→EW(x and living in single complex plane.
Supersymmetric Optical Structures
Miri, Mohammad-Ali; El-Ganainy, Ramy; Christodoulides, Demetrios N
2013-01-01
We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically construct index potentials capable of exhibiting the same scattering and guided wave characteristics. In particular, in the Helmholtz regime, we demonstrate that one-dimensional supersymmetric pairs display identical reflectivities and transmittivities for any angle of incidence. Optical SUSY is then extended to two-dimensional systems where a link between specific azimuthal mode subsets is established. Finally we explore supersymmetric photonic lattices where discreteness can be utilized to design lossless integrated mode filtering arrangements.
Supersymmetric Sneutrino-Higgs Inflation
Deen, Rehan; Purves, Austin
2016-01-01
It is shown that in the phenomenologically realistic supersymmetric $B-L$ MSSM theory, a linear combination of the neutral, up Higgs field with the third family left-and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order $10^{13}~\\mathrm{GeV}$, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.
Supersymmetric Sneutrino-Higgs inflation
Deen, Rehan; Ovrut, Burt A.; Purves, Austin
2016-11-01
It is shown that in the phenomenologically realistic supersymmetric B - L MSSM theory, a linear combination of the neutral, up Higgs field with the third family left- and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order 1013 GeV, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.
Approximate Flavor Symmetry in Supersymmetric Model
Tao, Zhijian
1998-01-01
We investigate the maximal approximate flavor symmetry in the framework of generic minimal supersymmetric standard model. We consider the low energy effective theory of the flavor physics with all the possible operators included. Spontaneous flavor symmetry breaking leads to the approximate flavor symmetry in Yukawa sector and the supersymmetry breaking sector. Fermion mass and mixing hierachies are the results of the hierachy of the flavor symmetry breaking. It is found that in this theory i...
Supersymmetric heterotic string backgrounds
Gran, U.; Papadopoulos, G.; Roest, D.; Cvetič, M.
2007-01-01
We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hep-th/0510176 and hep-th/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the het
New supersymmetric localizations from topological gravity
Bae, Jinbeom; Imbimbo, Camillo; Rey, Soo-Jong; Rosa, Dario
2016-03-01
Supersymmetric field theories can be studied exactly on off-shell "localizing" supergravity backgrounds. We show that these supergravity configurations can be identified with BRST invariant configurations of background topological gravity coupled to background topological gauge multiplets. We apply this topological point of view to two-dimensional {N}=left(2,2right) supersymmetric matter theories to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. We recover all known localizing backgrounds and (infinitely) many more that have not been explored so far. The newly found localizing backgrounds are characterized by quantized fluxes for both graviphotons of the {N}=left(2,2right) supergravity multiplet. The BRST invariant topological backgrounds are parametrized by both Killing vectors and {{S}}^1 -equivariant cohomology of the two-dimensional spacetime. We completely reconstruct the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are composite, in that they are nonlinear functionals of topological fields. Moreover, we show that the supersymmetric Ω-deformation is nothing but the background value of the ghost-for-ghost of topological gravity, a result which holds for higher dimensions too.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
Topological solitons in the supersymmetric Skyrme model
Gudnason, Sven Bjarke; Sasaki, Shin
2016-01-01
A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.
Supersymmetric branes on curved spaces and fluxes
Triendl, Hagen
2015-01-01
We discuss general supersymmetric brane configurations in flux backgrounds of string and M-theory and derive a necessary condition for the worldvolume theory to be supersymmetric on a given curved manifold. This condition resembles very much the conditions found from coupling a supersymmetric field theory to off-shell supergravity but can be derived in any dimension and for up to sixteen supercharges. Apart from the topological twist, all couplings appearing in the supersymmetry condition are linked to fluxes in the bulk. We explicitly derive the condition for D3-, M2- and M5-branes, in which case the results are also useful for constructing holographic duals to the corresponding field theories. In $N=1$ setups we compare the supersymmetry conditions to those that arise by coupling the field theory to off-shell supergravity. We find that the couplings of both old and new minimal supergravity are simultaneously realized, indicating that off-shell supergravity should be coupled via the S-multiplet of 16/16 supe...
Supersymmetric P(X,phi) and the Ghost Condensate
Khoury, Justin; Ovrut, Burt
2010-01-01
We show how to construct supersymmetric actions for higher-derivative scalar field theories of the form P(X,phi), within the context of d=4, N=1 supersymmetry. This construction is of general use, and is applied to write a supersymmetric version of the Dirac-Born-Infeld action. Our principal application of this formalism is to construct the supersymmetric extension of the ghost condensate. This allows us to study the interplay between supersymmetry, time-dependent backgrounds and violations of the null energy condition.
Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
DEFF Research Database (Denmark)
Arkani-Hamed, Nima; Bourjaily, Jacob L.; Cachazo, Freddy
2014-01-01
We present evidence that loop amplitudes in maximally supersymmetric (N=4) Yang-Mills theory (SYM) beyond the planar limit share some of the remarkable structures of the planar theory. In particular, we show that through two loops, the four-particle amplitude in full N=4 SYM has only logarithmic ...... singularities and is free of any poles at infinity—properties closely related to uniform transcendentality and the UV finiteness of the theory. We also briefly comment on implications for maximal (N=8) supergravity theory (SUGRA)....
On space of integrable quantum field theories
Smirnov, F. A.; Zamolodchikov, A. B.
2017-02-01
We study deformations of 2D Integrable Quantum Field Theories (IQFT) which preserve integrability (the existence of infinitely many local integrals of motion). The IQFT are understood as "effective field theories", with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (T T bar) built from the components of the energy-momentum tensor. The deformations of quantum field theories generated by X1 are "solvable" in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Gukov, S G
1997-01-01
The evidently supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta-function form the moduli space $M = RP^2$ where two types of phases were found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase which may be interpreted as a spin glass phase.
Decoupling of supersymmetric particles
Dobado, A; Peñaranda, S
1999-01-01
The possibility of a heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed in detail. The formal proof of decoupling of supersymmetric particles from low energy physics is stated in terms of the effective action for the particles of the Standard Model that results by integrating out all the sparticles in the limit where their masses are larger than the electroweak scale. The computation of the effective action for the standard electroweak gauge bosons W^{+-}, Z and \\gamma is performed by integrating out all the squarks, sleptons, charginos and neutralinos to one-loop. The Higgs sector is not considered in this paper. The large sparticle masses limit is also analyzed in detail. Explicit analytical formulae for the two-point functions of the electroweak gauge bosons to be valid in that limit are presented. Finally, the decoupling of sparticles in the S, T and U parameters is studied analitically. A discussion...
Reduction of couplings and finiteness in realistic supersymmetric GUTs
Energy Technology Data Exchange (ETDEWEB)
Kubo, J. [Kanazawa Univ. (Japan). Dept. of Physics; Mondragon, M. [Instituto de Fisica, UNAM, Apdo. Postal 20-364, Mexico 01000 D.F. (Mexico); Zoupanos, G. [Physics Dept., Nat. Technical University, 157 80 Zografou, Athens (Greece)
1997-07-01
Reduction of couplings in supersymmetric GUTs is achieved by searching for renormalization group invariant (RGI) relations among couplings which hold beyond the unification scale. Finiteness is due to the fact that there exist RGI relations among couplings that guarantee the vanishing of the {beta}-functions of a N = 1 supersymmetric GUT even to all orders in perturbation theory. Of particular interest are the relations among gauge and Yukawa couplings which lead to very interesting predictions of the top quark mass. (orig.).
Non-supersymmetric AdS and the Swampland
Ooguri, Hirosi
2016-01-01
We propose to sharpen the weak gravity conjecture by the statement that, except for BPS states in a supersymmetric theory, the gravitational force is strictly weaker than any electric force and provide a number of evidences for this statement. Our conjecture implies that any non-supersymmetric anti-de Sitter vacuum supported by fluxes must be unstable, as is the case for all known attempts at such holographic constructions.
Supersymmetric QCD: Exact Results and Strong Coupling
Dine, Michael; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-01-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is...
New Supersymmetric Localizations from Topological Gravity
Bae, Jinbeom; Rey, Soo-Jong; Rosa, Dario
2015-01-01
Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds. We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet. This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity. We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. The BRST invariant topological backgrounds are parametrized by both Killing vectors and $S^1$-equivariant cohomology of the 2-dimensional world-sheet. We reconstruct completely the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are "composite", i.e. they are non-linear functionals of them. We recover all the known localizing 2-dimensional backg...
Galoisian Approach to Supersymmetric Quantum Mechanics
Acosta-Humanez, Primitivo B
2009-01-01
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\\"odinger equation, specially the integrable cases in the sense of the Picard-Vessiot theory and the main algorithmic tools used here are the Kovacic algorithm and the \\emph{algebrization method} to obtain linear differential equations with rational coefficients. We analyze the Darboux transformations, Crum iterations and supersymmetric quantum mechanics with their \\emph{algebrized} versions from a Galoisian approach. Applying the algebrization method and the Kovacic's algorithm we obtain the ground state, the set of eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schr\\"odinger equation with potentials such as exactly solvable and shape invariant potentials. Finally, we introduce one methodology to find exactly solvable potentials: to construct other potentials, we apply the algebrization alg...
Supersymmetric composite gauge fields with compensators
Nishino, Hitoshi; Rajpoot, Subhash
2016-06-01
We study supersymmetric composite gauge theory, supplemented with compensator mechanism. As our first example, we give the formulation of N = 1 supersymmetric non-Abelian composite gauge theory without the kinetic term of a non-Abelian gauge field. The important ingredient is the Proca-Stueckelberg-type compensator scalar field that makes the gauge-boson field equation non-singular, i.e., the field equation can be solved for the gauge field algebraically as a perturbative expansion. As our second example, we perform the gauging of chiral-symmetry for N = 1 supersymmetry in four dimensions by a composite gauge field. These results provide supporting evidence for the consistency of the mechanism that combines the composite gauge field formulations and compensator formulations, all unified under supersymmetry.
On space of integrable quantum field theories
Directory of Open Access Journals (Sweden)
F.A. Smirnov
2017-02-01
Full Text Available We study deformations of 2D Integrable Quantum Field Theories (IQFT which preserve integrability (the existence of infinitely many local integrals of motion. The IQFT are understood as “effective field theories”, with finite ultraviolet cutoff. We show that for any such IQFT there are infinitely many integrable deformations generated by scalar local fields Xs, which are in one-to-one correspondence with the local integrals of motion; moreover, the scalars Xs are built from the components of the associated conserved currents in a universal way. The first of these scalars, X1, coincides with the composite field (TT¯ built from the components of the energy–momentum tensor. The deformations of quantum field theories generated by X1 are “solvable” in a certain sense, even if the original theory is not integrable. In a massive IQFT the deformations Xs are identified with the deformations of the corresponding factorizable S-matrix via the CDD factor. The situation is illustrated by explicit construction of the form factors of the operators Xs in sine-Gordon theory. We also make some remarks on the problem of UV completeness of such integrable deformations.
Perturbative stability along the supersymmetric directions of the landscape
Energy Technology Data Exchange (ETDEWEB)
Sousa, Kepa [Department of Theoretical Physics and History of Science, University of the Basque Country UPV/EHU, 48080 Bilbao (Spain); Ortiz, Pablo, E-mail: kepa.sousa@ehu.es, E-mail: ortiz@lorentz.leidenuniv.nl [Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, Niels Bohrweg 2, 2333 CA Leiden (Netherlands)
2015-02-01
We consider the perturbative stability of non-supersymmetric configurations in N=1 supergravity models with a spectator sector not involved in supersymmetry breaking. Motivated by the supergravity description of complex structure moduli in Large Volume Compactifications of type IIB-superstrings, we concentrate on models where the interactions are consistent with the supersymmetric truncation of the spectator fields, and we describe their couplings by a random ensemble of generic supergravity theories. We characterise the mass spectrum of the spectator fields in terms of the statistical parameters of the ensemble and the geometry of the scalar manifold. Our results show that the non-generic couplings between the spectator and the supersymmetry breaking sectors can stabilise all the tachyons which typically appear in the spectator sector before including the supersymmetry breaking effects, and we find large regions of the parameter space where the supersymmetric sector remains stable with probability close to one. We discuss these results about the stability of the supersymmetric sector in two physically relevant situations: non-supersymmetric Minkowski vacua, and slow-roll inflation driven by the supersymmetry breaking sector. For the class of models we consider, we have reproduced the regimes in which the KKLT and Large Volume Scenarios stabilise all supersymmetric moduli. We have also identified a new regime in which the supersymmetric sector is stabilised at a very robust type of dS minimum without invoking a large mass hierarchy.
Supersymmetric Electroweak Baryogenesis
Rius, N; Rius, Nuria; Sanz, Veronica
2000-01-01
We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, using a new method to compute the CP-violating asymmetry in the Higgsino flux reflected into the unbroken phase. The method is based on a Higgs insertion expansion. We find that the CP asymmetry at leading order is proportional to the change in $\\tan next-to-leading order this suppression factor disappears. These results explain previous discrepancies among different calculations, and may enhance the final baryon asymmetry generated during the electroweak phase transition.
Selecting Supersymmetric String Scenarios From Sparticle Spectra
Allanach, Benjamin C; Quevedo, Fernando
2002-01-01
We approach the following question: if supersymmetry is discovered, how can we select among different supersymmetric extensions of the Standard Model? In particular, we perform an analysis of the sparticle spectrum in low-energy string effective theories, asking which observables best distinguish various scenarios. We examine scenarios differing by the fundamental string scale and concentrate on GUT and intermediate scale models. We scan over all parameters (two goldstino angles, tan beta and the gravitino mass) in each scenario, finding ratios of sparticle masses that provide the maximum discrimination between them. The necessary accuracy for discrimination is determined in each case. We find that the required accuracy on various sparticle mass ratios is at the few percent level, a precision that may be achieved in future linear colliders. We place phenomenological constraints on the parameter space and determine the supersymmetric contribution to the muon anomalous magnetic moment.
Supersymmetric structure of the induced $W$ gravities
Ader, J P; Noirot, Y; Ader, Jean-Pierre; Biet, Franck; Noirot, Yves
1999-01-01
We derive the supersymmetric structure present in W-gravities which has been already observed in various contexts as Yang-Mills theory, topological field theories, bosonic string and chiral W_{3}-gravity. This derivation which is made in the geometrical framework of Zucchini, necessitates the introduction of an appropriate new basis of variables which replace the canonical fields and their derivatives. This construction is used, in the W_{2}-case, to deduce from the Chern-Simons action the Wess-Zumino-Polyakov action.
Supersymmetrizing Massive Gravity
Malaeb, Ola
2013-01-01
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering four N=1 chiral superfields with global Lorentz symmetry. When the scalar components of the chiral multiplets z^A acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. The global Lorentz index A becomes identified with the space-time Lorentz index making the scalar fields z^A vectors and the chiral spinors \\psi^A spin-3/2 Rarita-Schwinger fields. The global supersymmetry is promoted to a local one using the rules of tensor calculus of coupling the N=1 supergravity Lagrangian to the four chiral multiplets. We show that the spectrum of the model in the broken phase consists of a massive spin-2 field, two massive spin-3/2 fields with different mass and a massive vector.
Toward precision holography with supersymmetric Wilson loops
Faraggi, Alberto; Pando Zayas, Leopoldo A.; Silva, Guillermo A.; Trancanelli, Diego
2016-04-01
We consider certain 1/4 BPS Wilson loop operators in SU( N) N=4 supersymmetric Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in AdS 5 × S 5. The string on-shell action reproduces the large N and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by deriving the spectrum of quantum fluctuations around the classical string solution and by computing the corresponding 1-loop effective action. We discuss in detail the supermultiplet structure of the fluctuations. To remove a possible source of ambiguity in the ghost zero mode measure, we compare the 1/4 BPS configuration with the 1/2 BPS one, dual to a circular Wilson loop. We find a discrepancy between the string theory result and the gauge theory prediction, confirming a previous result in the literature. We are able to track the modes from which this discrepancy originates, as well as the modes that by themselves would give the expected result.
Supersymmetric mode converters
Heinrich, Matthias; Miri, Mohammad-Ali; Stützer, Simon; Nolte, Stefan; Szameit, Alexander; Christodoulides, Demetrios N.
2015-08-01
In recent years, the ever-increasing demand for high-capacity transmission systems has driven remarkable advances in technologies that encode information on an optical signal. Mode-division multiplexing makes use of individual modes supported by an optical waveguide as mutually orthogonal channels. The key requirement in this approach is the capability to selectively populate and extract specific modes. Optical supersymmetry (SUSY) has recently been proposed as a particularly elegant way to resolve this design challenge in a manner that is inherently scalable, and at the same time maintains compatibility with existing multiplexing strategies. Supersymmetric partners of multimode waveguides are characterized by the fact that they share all of their effective indices with the original waveguide. The crucial exception is the fundamental mode, which is absent from the spectrum of the partner waveguide. Here, we demonstrate experimentally how this global phase-matching property can be exploited for efficient mode conversion. Multimode structures and their superpartners are experimentally realized in coupled networks of femtosecond laser-written waveguides, and the corresponding light dynamics are directly observed by means of fluorescence microscopy. We show that SUSY transformations can readily facilitate the removal of the fundamental mode from multimode optical structures. In turn, hierarchical sequences of such SUSY partners naturally implement the conversion between modes of adjacent order. Our experiments illustrate just one of the many possibilities of how SUSY may serve as a building block for integrated mode-division multiplexing arrangements. Supersymmetric notions may enrich and expand integrated photonics by versatile optical components and desirable, yet previously unattainable, functionalities.
Leontaris, George K
1999-01-01
In the context of the free-fermionic formulation of the heterotic superstring, we construct a three-generation N = 1 supersymmetric SU(4) x SU(2) sub L x SU(2) sub R model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4,2 sub R) + (4-bar,2 sub R) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets imposes further restrictions to the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormaliz...
Supersymmetric Casimir Energy and $SL(3,\\mathbb{Z})$ Transformations
Brünner, Frederic; Spiridonov, Vyacheslav P
2016-01-01
We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an $SL(3,\\mathbb{Z})$ transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for $\\mathcal{N}=1$ SQCD and $\\mathcal{N}=4$ supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally.
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE
Institute of Scientific and Technical Information of China (English)
Xiao-wu Lu
2001-01-01
A class of finite difference methods of first- and second-order accuracy for the computa tion of solutions to the quasilinear wave equations is presented. These difference methods are constructed based on the symplectic schemes to the infinite-dimensional Hamiltonian system. Numerical experiments are presented to demonstrate the superior performance of these methods.
The Critical Properties of a Modulated Quantum sine-Gordon Model
Institute of Scientific and Technical Information of China (English)
WANG ZhiGuo; ZHANG YuMei
2002-01-01
A new procedure of trial variational wave functional is proposed for invostigating the mass reuormalizationand the local structure of the ground state of a one-dimensional quantum sine-Gorrdonm model with linear spatial modu-lation, whose ground state differs from that without modulation. Thc phase diagram obtained in parameters (αA 2,β2)plane shows that the vertical part of the boundary between soliton lattice phase and iucommensurate (IC) phase withvanishing gap sticks at β2 = 4, the IC phase can only appear forβ2 ＞ 47r and thc IC phase regime is enlarged withincreasing spatial modulation in the case of definite parameter αA-2. The transition is of the continuous type on thevertical part of the boundary, while it is of the first order on the boundary forβ2 ＞ 47r.
Massive sine-Gordon equation in the first few regions of collapse
Energy Technology Data Exchange (ETDEWEB)
Benfatto, G.; Gallavotti, G.; Nicolo, F.
1982-03-01
We study the ultraviolet stability problem for the two-dimensional Yukawa interaction lambda..integral..:cos ..cap alpha..phisub(xi):dxi in the region 4..pi.. < ..cap alpha../sup 2/ < anti..cap alpha../sup 2/, where 6..pi.. < anti..cap alpha../sup 3/ < 8..pi... The results have a natural Coulomb gas interpretation, because the counterterms do not depend on the field.
Supersymmetric quantum mechanics and paraquantization
Energy Technology Data Exchange (ETDEWEB)
Morchedi, O.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
The paraquantum Hamiltonian of a free particle is shown to be supersymmetric. Depending on the space-time dimension, the corresponding N=1 and N=2 supercharges are constructed and the related Hamiltonians are derived.
Energy Technology Data Exchange (ETDEWEB)
Leontaris, G.K.; Rizos, J
1999-08-09
In the context of the free-fermionic formulation of the heterotic superstring, we construct a three-generation N = 1 supersymmetric SU(4) x SU(2){sub L} x SU(2){sub R} model supplemented by an SU(8) hidden gauge symmetry and five Abelian factors. The symmetry breaking to the standard model is achieved using vacuum expectation values of a Higgs pair in (4,2{sub R}) + (4-bar,2{sub R}) at a high scale. One linear combination of the Abelian symmetries is anomalous and is broken by vacuum expectation values of singlet fields along the flat directions of the superpotential. All consistent string vacua of the model are completely classified by solving the corresponding system of F- and D-flatness equations including non-renormalizable terms up to sixth order. The requirement of existence of electroweak massless doublets imposes further restrictions to the phenomenologically viable vacua. The third generation fermions receive masses from the tree-level superpotential. Further, a complete calculation of all non-renormalizable fermion mass terms up to fifth order shows that in certain string vacua the hierarchy of the fermion families is naturally obtained in the model as the second and third generation fermions earn their mass from fourth- and fifth-order terms. Along certain flat directions it is shown that the ratio of the SU(4) breaking scale and the reduced Planck mass is equal to the up quark ratio ((m{sub c})/(m{sub t})) at the string scale. An additional prediction of the model, is the existence of a U(1) symmetry carried by the fields of the hidden sector, ensuring thus the stability of the lightest hidden state. It is proposed that the hidden states may account for the invisible matter of the universe.
Supersymmetric quantum mechanics with reflections
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Counting Trees in Supersymmetric Quantum Mechanics
Cordova, Clay
2015-01-01
We study the supersymmetric ground states of the Kronecker model of quiver quantum mechanics. This is the simplest quiver with two gauge groups and bifundamental matter fields, and appears universally in four-dimensional N=2 systems. The ground state degeneracy may be written as a multi-dimensional contour integral, and the enumeration of poles can be simply phrased as counting bipartite trees. We solve this combinatorics problem, thereby obtaining exact formulas for the degeneracies of an infinite class of models. We also develop an algorithm to compute the angular momentum of the ground states, and present explicit expressions for the refined indices of theories where one rank is small.
BiHermitian supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V Irnerio 46, I-40126 Bologna (Italy)
2007-04-21
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. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian Supersymmetric Quantum Mechanics
Zucchini, R
2006-01-01
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. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian supersymmetric quantum mechanics
Zucchini, Roberto
2007-04-01
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. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
Leptonic CP violation in supersymmetric standard model
Joshipura, A S
1995-01-01
We point out the possibility of spontaneous and hard CP-violation in the scalar potential of R-parity broken supersymmetric Standard Model. The existence of spontaneous CP-violation depends crucially on the R-parity breaking terms in the superpotential and, in addition, on the choice of the soft supersymmetry breaking terms. Unlike in theories with R-parity conservation, it is natural, in the context of the present model, for the sneutrinos to acquire (complex) vacuum expectation values. In the context of this model we examine here the global implications, like the strength of the CP-violating interactions and the neutrino masses.
Horvat, Raul; Trampetic, Josip; You, Jiangyang
2016-01-01
In this article we expound a discovery of the quantum equivalence/duality of U(N) noncommutative quantum field theories (NC QFT) related by the theta-exact Seiberg-Witten (SW) maps and at all orders in the perturbation theory with respect to the coupling constant. We show that this proof holds for Super Yang-Mills (SYM) theories with N=0,1,2,4$ supersymmetry. In short, Seiberg-Witten map does commute with the quantization of the U(N) NCQFT independently, with or without supersymmetry.
A review of Higgs mass calculations in supersymmetric models
DEFF Research Database (Denmark)
Draper, P.; Rzehak, H.
2016-01-01
related to the electroweak hierarchy problem. Perhaps the most extensively studied examples are supersymmetric models, which, while capable of producing a 125 GeV Higgs boson with SM-like properties, do so in non-generic parts of their parameter spaces. We review the computation of the Higgs mass...... in the Minimal Supersymmetric Standard Model, in particular the large radiative corrections required to lift mh to 125 GeV and their calculation via Feynman-diagrammatic and effective field theory techniques. This review is intended as an entry point for readers new to the field, and as a summary of the current...
Supersymmetric quantum mechanics on the lattice: I. Loop formulation
Directory of Open Access Journals (Sweden)
David Baumgartner
2015-05-01
Full Text Available Simulations of supersymmetric field theories on the lattice with (spontaneously broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N=2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper – the first in a series of three – we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.
Supersymmetric quantum mechanics on the lattice: I. Loop formulation
Baumgartner, David
2014-01-01
Simulations of supersymmetric field theories on the lattice with (spontaneously) broken supersymmetry suffer from a fermion sign problem related to the vanishing of the Witten index. We propose a novel approach which solves this problem in low dimensions by formulating the path integral on the lattice in terms of fermion loops. For N = 2 supersymmetric quantum mechanics the loop formulation becomes particularly simple and in this paper - the first in a series of three - we discuss in detail the reformulation of this model in terms of fermionic and bosonic bonds for various lattice discretisations including one which is Q-exact.
Rigid Supersymmetric Backgrounds of 3-dimensional Newton-Cartan Supergravity
Knodel, Gino; Liu, James T
2015-01-01
Recently, a non-relativistic off-shell formulation of three dimensional Newton-Cartan supergravity was proposed as the $c \\rightarrow \\infty$ limit of three dimensional $\\mathcal{N}=2$ supergravity in arXiv:1505.02095. In the present paper we study supersymmetric backgrounds within this theory. Using integrability constraints for the non-relativistic Killing spinor equations, we explicitly construct all maximally supersymmetric solutions, which admit four supercharges. In addition to these solutions, there are $\\frac{1}{2}$-BPS solutions with reduced supersymmetry. We give explicit examples of such backgrounds and derive necessary conditions for backgrounds preserving two supercharges. Finally, we address how supersymmetric backgrounds of $\\mathcal{N}=2$ supergravity are connected to the solutions found here in the $c \\rightarrow \\infty$ limit.
Supersymmetric Lepton Flavour Violation in Low-Scale Seesaw Models
Ilakovac, Amon
2009-01-01
We study a new supersymmetric mechanism for lepton flavour violation in \\mu and \\tau decays and \\mu -> e conversion in nuclei, within a minimal extension of the MSSM with low-mass heavy singlet neutrinos and sneutrinos. We find that the decays \\mu -> e\\gamma$, \\tau -> e\\gamma and \\tau -> \\mu\\gamma are forbidden in the supersymmetric limit of the theory, whereas other processes, such as \\mu -> eee, \\mu -> e conversion, \\tau -> eee and \\tau -> e\\mu\\mu, are allowed and can be dramatically enhanced several orders of magnitude above the observable level by potentially large neutrino Yukawa coupling effects. The profound implications of supersymmetric lepton flavour violation for present and future experiments are discussed.
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.
Supersymmetric quantum mechanics of the flux tube
Belitsky, A. V.
2016-12-01
The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow one to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl (2 | 1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their factorized form. The discussion corresponds to leading order of perturbation theory.
On supersymmetric Anti-de-Sitter, de-Sitter and Minkowski flux backgrounds
Gran, U; Papadopoulos, G
2016-01-01
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter spaces. We find that there are supersymmetric de Sitter solutions in supergravity theories including maximally supersymmetric ones in 10- and 11-dimensional supergravities. Moreover, warped flux Minkowski backgrounds can admit Killing spinors which are not Killing on the Minkowski subspace and therefore cannot be put in a factorized form.
A new supersymmetric classical Boussinesq equation
Institute of Scientific and Technical Information of China (English)
Zhang Meng-Xia; Liu Qing-Ping; Wang Juan; Wu Ke
2008-01-01
In this paper,we obtain a supersymmetric generalization for the classical Boussinesq equation.We show that the supersymmetric equation system passes the Painlevé test and we also calculate its one- and two-soliton solutions.
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
n = 4 supersymmetric FRW model
Energy Technology Data Exchange (ETDEWEB)
Rosales, J.J.; Pashnev, A. [Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 (Russian Federation); Tkach, V.I. [Instituto de Fisica, Universidad de Guanajuato, 05315-970 Leon, 66318 Guanajuato (Mexico)]. e-mail: juan@ifug3.ugto.mx, pashnev@thsun1.jinr.ru, vladimir@ifug3.ugto.mx
2003-07-01
In this work we have constructed the n = 4 extended local conformal time supersymmetry for the Friedmann-Robertson-Walker cosmological models. This is based on the superfield construction of the action, which is invariant under world line local n = 4 supersymmetry with SU(2){sub local} X SU(2){sub global} internal subgroup. It is shown that the supersymmetric action has the form of the localized (or superconformal) version of the action for n = 4 supersymmetric quantum mechanics. This superfield procedure provides a well defined scheme for including super matter. (Author)
Bilinear approach to the supersymmetric Gardner equation
Babalic, C. N.; Carstea, A. S.
2016-08-01
We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg-de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.
Approximations for strongly-coupled supersymmetric quantum mechanics
Kabat, D; Kabat, Daniel; Lifschytz, Gilad
2000-01-01
We advocate a set of approximations for studying the finite temperature behavior of strongly-coupled theories in 0+1 dimensions. The approximation consists of expanding about a Gaussian action, with the width of the Gaussian determined by a set of gap equations. The approximation can be applied to supersymmetric systems, provided that the gap equations are formulated in superspace. It can be applied to large-N theories, by keeping just the planar contribution to the gap equations. We analyze several models of scalar supersymmetric quantum mechanics, and show that the Gaussian approximation correctly distinguishes between a moduli space, mass gap, and supersymmetry breaking at strong coupling. Then we apply the approximation to a bosonic large-N gauge theory, and argue that a Gross-Witten transition separates the weak-coupling and strong-coupling regimes. A similar transition should occur in a generic large-N gauge theory, in particular in 0-brane quantum mechanics.
Consistent Perturbative Fixed Point Calculations in QCD and Supersymmetric QCD
DEFF Research Database (Denmark)
Ryttov, Thomas A.
2016-01-01
We suggest how to consistently calculate the anomalous dimension $\\gamma_*$ of the $\\bar{\\psi}\\psi$ operator in finite order perturbation theory at an infrared fixed point for asymptotically free theories. If the $n+1$ loop beta function and $n$ loop anomalous dimension are known then $\\gamma......_*$ can be calculated exactly and fully scheme independently through $O(\\Delta_f^n )$ where $\\Delta_f = \\bar{N_f} - N_f$ and $N_f$ is the number of flavors and $\\bar{N}_f$ is the number of flavors above which asymptotic freedom is lost. For a supersymmetric theory the calculation preserves supersymmetry...... order by order in $\\Delta_f$. We then compute $\\gamma_*$ through $O(\\Delta_f^2)$ for supersymmetric QCD in the $\\overline{\\text{DR}}$ scheme and find that it matches the exact known result. We find that $\\gamma_*$ is astonishingly well described in perturbation theory already at the few loops level...
Nonperturbative contributions from complexified solutions in C PN -1 models
Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
2016-11-01
We discuss the nonperturbative contributions from real and complex saddle point solutions in the C P1 quantum mechanics with fermionic degrees of freedom, using the Lefschetz thimble formalism beyond the Gaussian approximation. We find bion solutions, which correspond to (complexified) instanton-anti-instanton configurations stabilized in the presence of the fermionic degrees of freedom. By computing the one-loop determinants in the bion backgrounds, we obtain the leading order contributions from both the real and complex bion solutions. To incorporate quasizero modes which become nearly massless in a weak coupling limit, we regard the bion solutions as well-separated instanton-anti-instanton configurations and calculate a complexified quasimoduli integral based on the Lefschetz thimble formalism. The nonperturbative contributions from the real and complex bions are shown to cancel out in the supersymmetric case and give an (expected) ambiguity in the nonsupersymmetric case, which plays a vital role in the resurgent trans-series. For nearly supersymmetric situations, evaluation of the Lefschetz thimble gives results in precise agreement with those of the direct evaluation of the Schrödinger equation. We also perform the same analysis for the sine-Gordon quantum mechanics and point out some important differences showing that the sine-Gordon quantum mechanics does not correctly describe the 1d limit of the C PN -1 field theory of R ×S1.
Supersymmetric partition functions on Riemann surfaces
Benini, Francesco
2016-01-01
We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on $\\Sigma_g \\times T^n$ with partial topological twist on $\\Sigma_g$, where $\\Sigma_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on $\\Sigma_g \\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS4 whose horizon has $\\Sigma_g$ topology.
Supersymmetric backgrounds and generalised special holonomy
Coimbra, André; Strickland-Constable, Charles; Waldram, Daniel
2016-06-01
We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form {{{R}}}D-{1,1}× M. Using the language of {E}d(d)× {{{R}}}+ generalised geometry, we show that, for D≥slant 4, preserving minimal supersymmetry is equivalent to the manifold M having generalised special holonomy and list the relevant holonomy groups. We conjecture that this result extends to backgrounds preserving any number of supersymmetries. As a prime example, we consider { N }=1 in D = 4. The corresponding generalised special holonomy group is {SU}(7), giving the natural M theory extension to the notion of a G 2 manifold, and, for Type II backgrounds, reformulating the pure spinor {SU}(3)× {SU}(3) conditions as an integrable structure.
Supersymmetric Backgrounds and Generalised Special Holonomy
Coimbra, André; Waldram, Daniel
2014-01-01
We define intrinsic torsion in generalised geometry and use it to introduce a new notion of generalised special holonomy. We then consider generic warped supersymmetric flux compactifications of M theory and Type II of the form $\\mathbb{R}^{D-1,1}\\times M$. Using the language of $E_{d(d)}\\times\\mathbb{R}^+$ generalised geometry, we show that, for $D\\geq 4$, preserving minimal supersymmetry is equivalent to the manifold $M$ having generalised special holonomy and list the relevant holonomy groups. We conjecture that this result extends to backgrounds preserving any number of supersymmetries. As a prime example, we consider $\\mathcal{N}=1$ in $D=4$. The corresponding generalised special holonomy group is $SU(7)$, giving the natural M theory extension to the notion of a $G_2$ manifold, and, for Type II backgrounds, reformulating the pure spinor $SU(3)\\times SU(3)$ conditions as an integrable structure.
Consistent supersymmetric decoupling in cosmology
Sousa Sánchez, Kepa
2012-01-01
The present work discusses several problems related to the stability of ground states with broken supersymmetry in supergravity, and to the existence and stability of cosmic strings in various supersymmetric models. In particular we study the necessary conditions to truncate consistently a sector o
Supersymmetric classical mechanics: free case
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza]. E-mail: rafael@cfp.ufpb.br; Almeida, W. Pires de [Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza; Fonseca Neto, I. [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica
2001-06-01
We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, {phi}(t;{theta}). (author)
Bonelli, Giulio; Tanzini, Alessandro; Vasko, Petr
2014-01-01
We show that the exact partition function of U(N) six-dimensional gauge theory with eight supercharges on C^2 x S^2 provides the quantization of the integrable system of hydrodynamic type known as gl(N) periodic Intermediate Long Wave (ILW). We characterize this system as the hydrodynamic limit of elliptic Calogero-Moser integrable system. We compute the Bethe equations from the effective gauged linear sigma model on S^2 with target space the ADHM instanton moduli space, whose mirror computes the Yang-Yang function of gl(N) ILW. The quantum Hamiltonians are given by the local chiral ring observables of the six-dimensional gauge theory. As particular cases, these provide the gl(N) Benjamin-Ono and Korteweg-de Vries quantum Hamiltonians. In the four dimensional limit, we identify the local chiral ring observables with the conserved charges of Heisenberg plus W_N algebrae, thus providing a gauge theoretical proof of AGT correspondence.
Supersymmetric quantum mechanics of the flux tube
Belitsky, A V
2016-01-01
The Operator Product Expansion approach to scattering amplitudes in maximally supersymmetric gauge theory operates in terms of pentagon transitions for excitations propagating on a color flux tube. These obey a set of axioms which allow to determine them to all orders in 't Hooft coupling and confront against explicit calculations. One of the simplifying features of the formalism is the factorizability of multiparticle transitions in terms of single-particle ones. In this paper we extend an earlier consideration of a sector populated by one kind of excitations to the case of a system with fermionic as well as bosonic degrees of freedom to address the origin of the factorization. While the purely bosonic case was analyzed within an integrable noncompact open-spin chain model, the current case is solved in the framework of a supersymmetric sl(2|1) magnet. We find the eigenfunctions for the multiparticle system making use of the R-matrix approach. Constructing resulting pentagon transitions, we prove their facto...
Correlation functions of twist fields from Ward identities in the massive Dirac theory
Doyon, Benjamin
2011-01-01
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion point, and it is well-known that their vacuum two-point functions are determined by integrable differential equations. We extend part of this result to more general quantum states (pure or mixed) and to certain descendents, showing that some two-point functions are determined by the sinh-Gordon differential equations whenever there is translation and parity invariance, and the density matrix is the exponential of a bilinear expression in fermions. We use methods involving Ward identities associated to the copy-rotation symmetry in a model with two independent, anti-commuting copies. Such methods were used in the context of the thermally perturbed Ising quantum field theory model. We show that they are applicable to the Dirac theory as well, and we suggest that they are like...
Correlation functions of twist fields from Ward identities in the massive Dirac theory
Doyon, Benjamin; Silk, James
2011-07-01
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion point, and it is well-known that their vacuum two-point functions are determined by integrable differential equations. We extend part of this result to more general quantum states (pure or mixed) and to certain descendents, showing that some two-point functions are determined by the sinh-Gordon differential equations whenever there is translation and parity invariance, and the density matrix is the exponential of a bilinear expression in fermions. We use methods involving Ward identities associated to the copy-rotation symmetry in a model with two independent, anti-commuting copies. Such methods were used in the context of the thermally perturbed Ising quantum field theory model. We show that they are applicable to the Dirac theory as well, and we suggest that they are likely to have a much wider applicability to free fermion models in general. Finally, we note that our form-factor study of descendents twist fields combined with a CFT analysis provides a new way of evaluating vacuum expectation values of primary U(1) twist fields: by deriving and solving a recursion relation.
Correlation functions of twist fields from Ward identities in the massive Dirac theory
Energy Technology Data Exchange (ETDEWEB)
Doyon, Benjamin [Department of Mathematics, King' s College London, Strand WC2R 2LS (United Kingdom); Silk, James [Department of Mathematical Sciences, Durham University, Science Laboratories, South Road, Durham DH1 3LE (United Kingdom)
2011-07-22
We derive non-linear differential equations for correlation functions of U(1) twist fields in the two-dimensional massive Dirac theory. Primary U(1) twist fields correspond to exponential fields in the sine-Gordon model at the free-fermion point, and it is well-known that their vacuum two-point functions are determined by integrable differential equations. We extend part of this result to more general quantum states (pure or mixed) and to certain descendents, showing that some two-point functions are determined by the sinh-Gordon differential equations whenever there is translation and parity invariance, and the density matrix is the exponential of a bilinear expression in fermions. We use methods involving Ward identities associated to the copy-rotation symmetry in a model with two independent, anti-commuting copies. Such methods were used in the context of the thermally perturbed Ising quantum field theory model. We show that they are applicable to the Dirac theory as well, and we suggest that they are likely to have a much wider applicability to free fermion models in general. Finally, we note that our form-factor study of descendents twist fields combined with a CFT analysis provides a new way of evaluating vacuum expectation values of primary U(1) twist fields: by deriving and solving a recursion relation.
Penrose limit of a non-supersymmetric RG fixed point
Energy Technology Data Exchange (ETDEWEB)
Casero, Roberto E-mail: roberto.casero@mib.infn.it
2003-01-20
We extend the BMN duality between IIB superstring theory on a pp-wave background and a sector of N=4 super Yang-Mills theory to the non-supersymmetric and unstable background built by Romans as a compactification on a U(1) bundle over CP{sup 2} with 3-form and 5-form field strength fluxes. We obtain a stable theory with the fewest number of supercharges (e.g., 16) allowed by this kind of solutions and make conjectures on the dual gauge theory.
Penrose limit of a non--supersymmetric RG fixed point
Casero, R
2003-01-01
We extend the BMN duality between IIB superstring theory on a pp--wave background and a sector of N=4 super Yang-Mills theory to the non--supersymmetric and unstable background built by Romans as a compactification on a U(1) bundle over CP2 with 3--form and 5--form field strength fluxes. We obtain a stable theory with the fewest number of supercharges (e.g. 16) allowed by this kind of solutions and make conjectures on the dual gauge theory.
Tian, Kai; Liu, Q. P.
2012-07-01
A new N=1 supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed.
Precision Holography with Supersymmetric Wilson Loops
Faraggi, Alberto; Silva, Guillermo A; Trancanelli, Diego
2016-01-01
We consider certain 1/4 BPS Wilson loop operators in $SU(N)$ ${\\cal N}=4$ super Yang-Mills theory, whose expectation value can be computed exactly via supersymmetric localization. Holographically, these operators are mapped to fundamental strings in $AdS_5\\times S^5$. The string on-shell action reproduces the large $N$ and large coupling limit of the gauge theory expectation value and, according to the AdS/CFT correspondence, there should also be a precise match between subleading corrections to these limits. We perform a test of such match at next-to-leading order in string theory, by computing the 1-loop determinant of the quantum fluctuations around the classical string configuration. A source of ambiguity, related to ghost zero modes, is removed by comparing our operator with the 1/2 BPS circular Wilson loop. We find perfect agreement between the string theory result and the gauge theory prediction. This successful match, besides being a high precision test of the AdS/CFT correspondence, elucidates some o...
The supersymmetric NUTs and bolts of holography
Energy Technology Data Exchange (ETDEWEB)
Martelli, Dario; Passias, Achilleas [Department of Mathematics, King' s College London, The Strand, London WC2R 2LS (United Kingdom); Sparks, James [Mathematical Institute, University of Oxford, 24-29 St Giles' , Oxford OX1 3LB (United Kingdom)
2013-11-21
We show that a given conformal boundary can have a rich and intricate space of supersymmetric supergravity solutions filling it, focusing on the case where this conformal boundary is a biaxially squashed Lens space. Generically we find that the biaxially squashed Lens space S{sup 3}/Z{sub p} admits Taub-NUT-AdS fillings, with topology R{sup 4}/Z{sub p}, as well as smooth Taub-Bolt-AdS fillings with non-trivial topology. We show that the Taub-NUT-AdS solutions always lift to solutions of M-theory, and correspondingly that the gravitational free energy then agrees with the large N limit of the dual field theory free energy, obtained from the localized partition function of a class of N=2 Chern–Simons-matter theories. However, the solutions of Taub-Bolt-AdS type only lift to M-theory for appropriate classes of internal manifold, meaning that these solutions exist only for corresponding classes of three-dimensional N=2 field theories.
Simple supersymmetric strongly coupled preon model
Fajfer, S.; Tadić, D.
1988-08-01
This supersymmetric-SU(5) composite model is a natural generalization of the usual strong-coupling models. Preon superfields are in representations 5* and 10. The product representations 5*×10, 5×10, 5×5, and 5*×5 contain only those strongly hypercolor bound states which are needed in the standard electroweak theory. There are no superfluous quarklike states. The neutrino is massless. Only one strongly hypercolor bound singlet (10×10*) can exist as a free particle. At higher energies one should expect to see a plethora of new particles. Grand unification happens at the scale M~1014 GeV. Cabibbo mixing can be incorporated by using a transposed Kobayashi-Maskawa mixing matrix.
Supersymmetric Wilson loops at two loops
Bassetto, Antonio; Pucci, Fabrizio; Seminara, Domenico
2008-01-01
We study the quantum properties of certain BPS Wilson loops in ${\\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.
Signals of Supersymmetric Dark Matter
Abbas, A
2000-01-01
The Lightest Supersymmetric Particle predicted in most of the supersymmetric scenarios is an ideal candidate for the dark matter of cosmology. Their detection is of extreme significance today. Recently there have been intriguing signals of a 59 Gev neutralino dark matter at DAMA in Gran Sasso. We look at other possible signatures of dark matter in astrophysical and geological frameworks. The passage of the earth through dense clumps of dark matter would produce large quantities of heat in the interior of this planet through the capture and subsequent annihilation of dark matter particles. This heat would lead to large-scale volcanism which could in turn have caused mass extinctions. The periodicity of such volcanic outbursts agrees with the frequency of palaeontological mass extinctions as well as the observed periodicity in the occurrence of the largest flood basalt provinces on the globe. Binary character of these extinctions is another unique aspect of this signature of dark matter. In addition dark matter...
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.
On timelike supersymmetric solutions of gauged minimal 5-dimensional supergravity
Chimento, Samuele
2016-01-01
We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the K\\"ahler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple second-order differential equation. Using this general form of the base space, the equations satisfied by the building blocks of the solutions become of, at most, fourth degree and can be solved by simple polynomic ansatzs. In this way we construct two 3-parameter families of solutions that contain almost all the timelike supersymmetric solutions of this theory with one angular momentum known so far and a few more: the (singular) supersymmetric Reissner-Nordstr\\"om-AdS solutions, the three exact supersymmetric solutions describing the three near-horizon geometries found by Gutowski and Reall, three 1-parameter asymptotically-AdS$_{5}$ black-hole solutions with those three near-horizon geometries (Gutowski and Reall's black hole being one of them), three generalizations of the G\\"odel un...
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
Equivalence between a bosonic theory and a massive non-local Thirring model at Finite Temperature
Manias, M V
1998-01-01
Using the path-integral bosonization procedure at Finite Temperature we study the equivalence between a massive Thirring model with non-local interaction between currents (NLMT) and a non-local extension of the sine-Gordon theory (NLSG). To this end we make a perturbative expansion in the mass parameter of the NLMT model and in the cosine term of the NLSG theory in order to obtain explicit expressions for the corresponding partition functions. We conclude that for certain relationship between NLMT and NLSG potentials both the fermionic and bosonic expansions are equal term by term. This result constitutes a generalization of Coleman's equivalence at T=0, when considering a Thirring model with bilocal potentials in the interaction term at Finite Temperature. The study of this model is relevant in connection with the physics of strongly correlated systems in one spatial dimension. Indeed, in the language of many-body non-relativistic systems, the relativistic mass term can be shown to represent the introduction...
Non-linear magnetization effects within the Kosterlitz-Thouless theory
Benfatto, Lara; Castellani, Claudio; Giamarchi, Thierry
2008-03-01
Recent experiments in cuprate superconductors have attracted the attention on the role of vortex fluctuations. Measurements of the field-induced magnetization showed that the correlation length diverge exponentially, as predicted within the Kosterlitz-Thouless (KT) theory. However, it is somehow puzzling thepersistence of strong non-linear magnetization effects at low field. Here we address this issue by means of a new theoretical approach to the KT transition at finite magnetic field, based on the sine-Gordon model. This approach is particularly useful in two respects. First, it leads to a straightforward definition of the field-induced magnetization as a function of the external magnetic field H instead of the magnetic induction B, which is crucial to get a consistent description of the Meissner phase. Second, it allows us to identify the cross-over field Hcr from linear to non-linear magnetization both below and above the transition. Above TKT Hcr turns out to scale as the inverse correlation length, so that it decreases as the transition is approached. As a consequence, the fact that only the non-linear regime is accessible experimentally should be interpreted as a typical signature of the fast divergence of the correlation length within the KT theory. L.Benfatto, C.Castellani and T.Giamarchi, Phys. Rev. Lett. 99, 207002 (2007)
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
Supersymmetric partition functions and the three-dimensional A-twist arXiv
Closset, Cyril; Willett, Brian
We study three-dimensional $\\mathcal{N}=2$ supersymmetric gauge theories on $\\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\\Sigma_g$. We compute the $\\mathcal{M}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2 \\times S^1$ with a topological twist. More generally, we show that the 3d $\\mathcal{N}=2$ supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on $\\mathcal{M}_{g,p}$ are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimens...
Electric Dipole Moments of Neutron and Electron in Supersymmetric Model
Aoki, Mayumi; Kadoyoshi, Tomoko; Sugamoto, Akio; Oshimo, Noriyuki
1997-01-01
The electric dipole moments (EDMs) of the neutron and the electron are reviewed within the framework of the supersymmetric standard model (SSM) based on grand unified theories coupled to N=1 supergravity. Taking into account one-loop and two-loop contributions to the EDMs, we explore SSM parameter space consistent with experiments and discuss predicted values for the EDMs. Implications of baryon asymmetry of our universe for the EDMs are also discussed.
Latest results from lattice N=4 supersymmetric Yang--Mills
Schaich, David; Damgaard, Poul H; Giedt, Joel
2016-01-01
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
Loop formulation of supersymmetric Yang-Mills quantum mechanics
Steinhauer, Kyle
2014-01-01
We derive the fermion loop formulation of N=4 supersymmetric SU(N) Yang-Mills quantum mechanics on the lattice. The loop formulation naturally separates the contributions to the partition function into its bosonic and fermionic parts with fixed fermion number and provides a way to control potential fermion sign problems arising in numerical simulations of the theory. Furthermore, we present a reduced fermion matrix determinant which allows the projection into the canonical sectors of the theory and hence constitutes an alternative approach to simulate the theory on the lattice.
Computing Maximally Supersymmetric Scattering Amplitudes
Stankowicz, James Michael, Jr.
This dissertation reviews work in computing N = 4 super-Yang--Mills (sYM) and N = 8 maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetime dimensions in novel ways. After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples. In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneous cut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4. In Ch. 5, the three-loop four-point amplitude is presented in the d log representation and in the pure integrand representation. In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at
Supersymmetric Perturbations of the M5 brane
Niarchos, Vasilis
2014-01-01
We study long-wavelength supersymmetric deformations of brane solutions in supergravity using an extension of previous ideas within the general scheme of the blackfold approach. As a concrete example, we consider long-wavelength perturbations of the planar M2-M5 bound state solution in eleven-dimensional supergravity. We propose a specific ansatz for the first order deformation of the supergravity fields and explore how this deformation perturbs the Killing spinor equations. We find that a special part of these equations gives a projection equation on the Killing spinors that has the same structure as the $\\kappa$-symmetry condition of the abelian M5 brane theory. Requiring a match between supergravity and gauge theory implies a specific non-linear gauge-gravity map between the bosonic fields of the abelian M5 brane theory and the gravity-induced fluid-like degrees of freedom of the blackfold equations that control the perturbative gravity solution. This observation sheds new light on the SUGRA/DBI correspond...
Supersymmetric plasma systems and their nonsupersymmetric counterparts
Czajka, Alina
2016-01-01
In this thesis a systematic comparison of supersymmetric plasma systems and their nonsupersymmetric counterparts is presented. The work is motivated by the AdS/CFT correspondence and the main aim is to check how much the plasma governed by the N=4 super Yang-Mills theory resembles the quark-gluon plasma studied experimentally in relativistic heavy-ion collisions. The analysis is done in a weak coupling regime where perturbative methods are applicable. Since the Keldysh-Schwinger approach is used, not only equilibrium but also nonequilibrium plasmas, which are assumed to be ultrarelativistic, are under consideration. First, using the functional techniques we introduce Faddeev-Popov ghosts into the Keldysh-Schwinger formalism of nonAbelian gauge theories. Next the collective excitations of the N=1 SUSY QED plasma are considered and compared to those of the usual QED system. The analysis is repeated to confront with each other the plasmas governed by the N=4 super Yang-Mills and QCD theories. Finally, transport ...
Destri, C
1994-01-01
We present a unified approach to the Thermodynamic Bethe Ansatz (TBA) for magnetic chains and field theories that includes the finite size (and zero temperature) calculations for lattice BA models. In all cases, the free energy follows by quadratures from the solution of a {\\bf single} non-linear integral equation (NLIE). [A system of NLIE appears for nested BA]. We derive the NLIE for: a) the six-vertex model with twisted boundary conditions; b) the XXZ chain in an external magnetic field h_z and c) the sine-Gordon-massive Thirring model (sG-mT) in a periodic box of size \\b \\equiv 1/T using the light-cone approach. This NLIE is solved by iteration in one regime (high T in the XXZ chain and low T in the sG-mT model). In the opposite (conformal) regime, the leading behaviors are obtained in closed form. Higher corrections can be derived from the Riemann-Hilbert form of the NLIE that we present.