Phases of chiral gauge theories
International Nuclear Information System (INIS)
We discuss the behavior of two non-supersymmetric chiral SU(N) gauge theories, involving fermions in the symmetric and antisymmetric two-index tensor representations respectively. In addition to global anomaly matching, we employ a recently proposed inequality constraint on the number of effective low energy (massless) degrees of freedom of a theory, based on the thermodynamic free energy. Several possible zero temperature phases are consistent with the constraints. A simple picture for the phase structure emerges if these theories choose the phase, consistent with global anomaly matching, that minimizes the massless degree of freedom count defined through the free energy. This idea suggests that confinement with the preservation of the global symmetries through the formation of massless composite fermions is in general not preferred. While our discussion is restricted mainly to bilinear condensate formation, higher dimensional condensates are considered for one case. We conclude by commenting briefly on two related supersymmetric chiral theories. (c) 2000 The American Physical Society
Chiral gauge theories on a lattice
International Nuclear Information System (INIS)
The authors formulate a chiral gauge invariant theory of lattice fermions by introducing extra degrees of freedom. It is applied to the chiral U(1) gauge theories in two and four dimensions and the effective actions of the gauge fields are calculated which indicate the mass generation of the gauge bosons. The difficulty is pointed out to execute the perturbation with a finite gauge boson mass in four dimensions
A Nonperturbative Regulator for Chiral Gauge Theories
Grabowska, Dorota M
2015-01-01
We propose a nonperturbative gauge invariant regulator for $d$-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in $d+1$ dimensions with quantum gauge fields that reside on one $d$-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local $d$-dimensional interpretation if and only if the chiral fermion representation is anomaly free. A physical realization of this construction leads to mirror fermions in the Standard Model with soft form factors for gauge fields and gravity. These mirror particles could evade detection except by sensitive probes at extremely low energy, and yet still affect vacuum topology, and could gravitate differently than conventional matter.
Nonperturbative Regulator for Chiral Gauge Theories?
Grabowska, Dorota M; Kaplan, David B
2016-05-27
We propose a nonperturbative gauge-invariant regulator for d-dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d+1 dimensions with quantum gauge fields that reside on one d-dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d-dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter. PMID:27284646
Nonperturbative Regulator for Chiral Gauge Theories?
Grabowska, Dorota M.; Kaplan, David B.
2016-05-01
We propose a nonperturbative gauge-invariant regulator for d -dimensional chiral gauge theories on the lattice. The method involves simulating domain wall fermions in d +1 dimensions with quantum gauge fields that reside on one d -dimensional surface and are extended into the bulk via gradient flow. The result is a theory of gauged fermions plus mirror fermions, where the mirror fermions couple to the gauge fields via a form factor that becomes exponentially soft with the separation between domain walls. The resultant theory has a local d -dimensional interpretation only if the chiral fermion representation is anomaly free. A physical realization of this construction would imply the existence of mirror fermions in the standard model that are invisible except for interactions induced by vacuum topology, and which could gravitate differently than conventional matter.
Chiral symmetry and lattice gauge theory
International Nuclear Information System (INIS)
I review the problem of formulating chiral symmetry in lattice gauge theory. I discuss recent approaches involving an infinite tower of additional heavy states to absorb Fermion doublers. For hadronic physics this provides a natural scheme for taking quark masses to zero without requiring a precise tuning of parameters. A mirror Fermion variation provides a possible way of extending the picture to chirally coupled light Fermions
Target Spaces from Chiral Gauge Theories
Melnikov, Ilarion V; Sethi, Savdeep; Stern, Mark
2012-01-01
Chiral gauge theories in two dimensions with (0,2) supersymmetry are central in the study of string compactifications. Remarkably little is known about generic (0,2) theories. We consider theories with branches on which multiplets with a net gauge anomaly become massive. The simplest example is a relevant perturbation of the gauge theory that flows to the CP(n) model. To compute the effective action, we derive a useful set of Feynman rules for (0,2) supergraphs. From the effective action, we see that the infra-red geometry reflects the gauge anomaly by the presence of a boundary at finite distance. In generic examples, there are boundaries, fluxes and branes; the resulting spaces are non-Kahler.
Regularized path integrals and anomalies -- U(1) chiral gauge theory
Kopper, Christoph; Lévêque, Benjamin
2011-01-01
We analyse the origin of the Adler anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [1]. Here we analyse U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-p...
CP breaking in lattice chiral gauge theories
International Nuclear Information System (INIS)
The CP symmetry is not manifestly implemented for the local and doubler-free Ginsparg-Wilson operator in lattice chiral gauge theory. We precisely identify where the effects of this CP breaking appear. We show that they appear in: (I) Overall constant phase of the fermion generating functional. (II) Overall constant coefficient of the fermion generating functional. (III) Fermion propagator appearing in external fermion lines and the propagator connected to Yukawa vertices. The first effect appears from the transformation of the path integral measure and it is absorbed into a suitable definition of the constant phase factor for each topological sector; in this sense there appears no 'CP anomaly'. The second constant arises from the explicit breaking in the action and it is absorbed by the suitable weights with which topological sectors are summed. The last one in the propagator is inherent to this formulation and cannot be avoided by a mere modification of the projection operator, for example, in the framework of the Ginsparg-Wilson operator. This breaking emerges as an (almost) contact term in the propagator when the Higgs field, which is treated perturbatively, has no vacuum expectation value. In the presence of the vacuum expectation value, however, a completely new situation arises and the breaking becomes intrinsically non-local, though this breaking may still be removed in a suitable continuum limit. This non-local CP breaking is expected to persist for a non-perturbative treatment of the Higgs coupling. (author)
On the overlap formulation of chiral gauge theory
International Nuclear Information System (INIS)
The overlap formula proposed by Narayanan and Neuberger in chiral gauge theories is examined. The free chiral and Dirac Green's functions are constructed in this formalism. Four dimensional anomalies are calculated and the usual anomaly cancellation for one standard family of quarks and leptons is verified. (author). 4 refs
SU(N) chiral gauge theories on the lattice
International Nuclear Information System (INIS)
We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-Abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the Abelian case. The new ingredient allowing us to deal with the non-Abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-Abelian group (which we will take to be SU(N)) down to its maximal Abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining Abelian gauge symmetry. This modifies the equivariant Becchi-Rouet-Stora-Tyutin (BRST) identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the Abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be added to the lattice gauge-fixing action in order to have access to the desired critical point in the phase diagram. We argue that gauge invariance is restored in the continuum limit by adjusting a finite number of counter terms. We emphasize that weak-coupling perturbation theory applies at the critical point which defines the continuum limit of our lattice chiral gauge theory
Chiral rings and anomalies in supersymmetric gauge theory
International Nuclear Information System (INIS)
Motivated by recent work of Dijkgraaf and Vafa, we study anomalies and the chiral ring structure in a supersymmetric U(N) gauge theory with an adjoint chiral superfield and an arbitrary superpotential. A certain generalization of the Konishi anomaly leads to an equation which is identical to the loop equation of a bosonic matrix model. This allows us to solve for the expectation values of the chiral operators as functions of a finite number of 'integration constants'. From this, we can derive the Dijkgraaf-Vafa relation of the effective superpotential to a matrix model. Some of our results are applicable to more general theories. For example, we determine the classical relations and quantum deformations of the chiral ring of N=1 super Yang-Mills theory with SU(N) gauge group, showing, as one consequence, that all supersymmetric vacua of this theory have a nonzero chiral condensate. (author)
Removal of chiral anomalies in abelian gauge theories
International Nuclear Information System (INIS)
It is shown that chiral anomalies can be removed in abelian gauge theories. After a discussion of the two dimensional case where exact solutions are available we study the four dimensional theory. We use perturbation theory, i.e. analyse the triangle Feynman integrals, and determine the general subtraction structure of the gauge current. Then we show that gauges exist for which current conservation holds and the theory is gauge invariant. As far as the generating functional is concerned the anomaly is employed first as gauge fixing condition. After rewriting the interaction in a gauge invariant form the gauge fixing condition can be imposed as usual. In our approach the integration over the gauge group remains trivial. (author)
Ward identities and gauge independence in general chiral gauge theories
Anselmi, Damiano
2015-01-01
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized $\\Gamma $ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized $\\Gamma $ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on...
Ward identities and gauge independence in general chiral gauge theories
Anselmi, Damiano
2015-07-01
Using the Batalin-Vilkovisky formalism, we study the Ward identities and the equations of gauge dependence in potentially anomalous general gauge theories, renormalizable or not. A crucial new term, absent in manifestly nonanomalous theories, is responsible for interesting effects. We prove that gauge invariance always implies gauge independence, which in turn ensures perturbative unitarity. Precisely, we consider potentially anomalous theories that are actually free of gauge anomalies thanks to the Adler-Bardeen theorem. We show that when we make a canonical transformation on the tree-level action, it is always possible to re-renormalize the divergences and re-fine-tune the finite local counterterms, so that the renormalized Γ functional of the transformed theory is also free of gauge anomalies, and is related to the renormalized Γ functional of the starting theory by a canonical transformation. An unexpected consequence of our results is that the beta functions of the couplings may depend on the gauge-fixing parameters, although the physical quantities remain gauge independent. We discuss nontrivial checks of high-order calculations based on gauge independence and determine how powerful they are.
Regularized path integrals and anomalies: U(1) chiral gauge theory
International Nuclear Information System (INIS)
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Mueller, V. F., 'Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations', Rev. Math. Phys. 21, 781 (2009)]. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
Shi, Yan-Liang
2016-01-01
We analyze patterns of dynamical symmetry breaking in strongly coupled chiral gauge theories with direct-product gauge groups $G$. If the gauge coupling for a factor group $G_i \\subset G$ becomes sufficiently strong, it can produce bilinear fermion condensates that break the $G_i$ symmetry itself and/or break other gauge symmetries $G_j \\subset G$. Our comparative study of a number of strongly coupled direct-product chiral gauge theories elucidates how the patterns of symmetry breaking depend on the structure of $G$ and on the relative sizes of the gauge couplings corresponding to factor groups in the direct product.
Tumbling and complementarity in a chiral gauge theory
International Nuclear Information System (INIS)
We consider in detail a chiral SU(N) gauge theory which undergoes multiple tumbling. An extension of the notion of complementarity is used which allows us to deduce the set of massless fermions, in the confining phase of the theory, which we needed for anomaly matching. The liklehood of this confining phase ever being realized in practice is discussed. (orig.)
A Wilson-Majorana regularization for lattice chiral gauge theories
International Nuclear Information System (INIS)
We discuss the regularization of chiral gauge theories on the lattice introducing only physical degrees of freedom. This is obtained by writing the Wilson term in a Majorana form, at the expense of the U(1) symmetry related to fermion number conservation. The idea of restoring chiral invariance in the continuum by introducing a properly chosen set of counterterms to be added to the tree level action is checked against one-loop perturbative calculations. (orig.)
Phases of N=1 Supersymmetric Chiral Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Craig, Nathaniel; /Princeton, Inst. Advanced Study /Rutgers U., Piscataway; Essig, Rouven; /Princeton, Inst. Advanced Study /YITP, Stony Brook /SLAC /Stanford U., Phys. Dept.; Hook, Anson; Torroba, Gonzalo; /SLAC /Stanford U., Phys. Dept.
2012-02-17
We analyze the phases of supersymmetric chiral gauge theories with an antisymmetric tensor and (anti)fundamental flavors, in the presence of a classically marginal superpotential deformation. Varying the number of flavors that appear in the superpotential reveals rich infrared chiral dynamics and novel dualities. The dualities are characterized by an infinite family of magnetic duals with arbitrarily large gauge groups describing the same fixed point, correlated with arbitrarily large classical global symmetries that are truncated nonperturbatively. At the origin of moduli space, these theories exhibit a phase with confinement and chiral symmetry breaking, an interacting nonabelian Coulomb phase, and phases where an interacting sector coexists with a sector that either s-confines or is in a free magnetic phase. Properties of these intriguing 'mixed phases' are studied in detail using duality and a-maximization, and the presence of superpotential interactions provides further insights into their formation.
SU(N) chiral gauge theories on the lattice
Golterman, M F L; Golterman, Maarten; Shamir, Yigal
2004-01-01
We extend the construction of lattice chiral gauge theories based on non-perturbative gauge fixing to the non-abelian case. A key ingredient is that fermion doublers can be avoided at a novel type of critical point which is only accessible through gauge fixing, as we have shown before in the abelian case. The new ingredient allowing us to deal with the non-abelian case as well is the use of equivariant gauge fixing, which handles Gribov copies correctly, and avoids Neuberger's no-go theorem. We use this method in order to gauge fix the non-abelian group (which we will take to be SU(N)) down to its maximal abelian subgroup. Obtaining an undoubled, chiral fermion content requires us to gauge-fix also the remaining abelian gauge symmetry. This modifies the equivariant BRST identities, but their use in proving unitarity remains intact, as we show in perturbation theory. On the lattice, equivariant BRST symmetry as well as the abelian gauge invariance are broken, and a judiciously chosen irrelevant term must be ad...
U(1) chiral gauge theory on lattice with gauge-fixed domain wall fermions
International Nuclear Information System (INIS)
We investigate a U(1) lattice chiral gauge theory (LξGT) with domain wall fermions and gauge fixing. In the reduced model limit, our perturbative and numerical investigations at Yukawa coupling y = 1 show that there are no extra mirror chiral modes. The longitudinal gauge degrees of freedom have no effect on the free domain wall fermion spectrum consisting of opposite chiral modes at the domain wall and the anti-domain wall which have an exponentially damped overlap. Our numerical investigation at small Yukawa couplings (y << 1) also leads to similar conclusions as above
New tests of the gauge-fixing approach to lattice chiral gauge theories
International Nuclear Information System (INIS)
We report on recent progress with the gauge-fixing approach to lattice chiral gauge theories. The bosonic sector of the gauge-fixing approach is studied with fully dynamical U(1) gauge fields. We demonstrate that it is important to formulate the Lorentz gauge-fixing action such that the dense set of lattice Gribov copies is removed, and the gauge-fixing action has a unique absolute minimum. We then show that the spectrum in the continuum limit contains only the desired massless photon, as expected
Regularized path integrals and anomalies: U(1) chiral gauge theory
Kopper, Christoph; Lévêque, Benjamin
2012-02-01
We analyze the origin of the Adler-Bell-Jackiw anomaly of chiral U(1) gauge theory within the framework of regularized path integrals. Momentum or position space regulators allow for mathematically well-defined path integrals but violate local gauge symmetry. It is known how (nonanomalous) gauge symmetry can be recovered in the renormalized theory in this case [Kopper, C. and Müller, V. F., "Renormalization of spontaneously broken SU(2) Yang-Mills theory with flow equations," Rev. Math. Phys. 21, 781 (2009)], 10.1142/S0129055X0900375X. Here we analyze U(1) chiral gauge theory to show how the appearance of anomalies manifests itself in such a context. We show that the three-photon amplitude leads to a violation of the Slavnov-Taylor identities which cannot be restored on taking the UV limit in the renormalized theory. We point out that this fact is related to the nonanalyticity of this amplitude in the infrared region.
Chiral rings and phases of supersymmetric gauge theories
International Nuclear Information System (INIS)
We solve for the expectation values of chiral operators in supersymmetric U(N) gauge theories with matter in the adjoint, fundamental and anti-fundamental representations. A simple geometric picture emerges involving a description by a meromorphic one-form on a Riemann surface. The equations of motion are equivalent to a condition on the integrality of periods of this form. The solution indicates that all semiclassical phases with the same number of U(1) factors are continuously connected. (author)
Chiral Bosons as solutions of the BV master equation 2D chiral gauge theories
Braga, N. R. F.; Montani, H.
1994-01-01
We construct the chiral Wess-Zumino term as a solution for the Batalin-Vilkovisky master equation for anomalous two-dimensional gauge theories, working in an extended field-antifield space, where the gauge group elements are introduced as additional degrees of freedom. We analyze the Abelian and the non-Abelian cases, calculating in both cases the BRST generator in order to show the physical equivalence between this chiral solution for the master equation and the usual (non-chiral) one.
Lattice regularization of chiral gauge theories to all orders of perturbation theory
Lüscher, Martin
2000-01-01
In the framework of perturbation theory, it is possible to put chiral gauge theories on the lattice without violating the gauge symmetry or other fundamental principles, provided the fermion representation of the gauge group is anomaly-free. The basic elements of this construction (which starts from the Ginsparg-Wilson relation) are briefly recalled and the exact cancellation of the gauge anomaly, at any fixed value of the lattice spacing and for any compact gauge group, is then proved rigoro...
Chiral symmetry aspects in supersymmetric confining gauge theories
International Nuclear Information System (INIS)
We provide a detailed analysis of the interplay between chiral symmetry and supersymmetry within the context of supersymmetric confining gauge theories. We describe a general method leading to exact results on quark mass dependences of physical quantities such as bound-state masses, bilinear condensates,... We also establish the commutation relations satisfied by the supersymmetric and chiral charges in presence of the soft breaking due to quark masses. We show that, if the chiral limit is unique, the global SUsub(L)(Nsub(f)) x SUsub(R)(Nsub(f)) symmetry is not spontaneously broken. If this limit is not unique, a spontaneous breakdown of the axial symmetry is allowed, but only at the cost of a simultaneous breakdown of the vector symmetry
Six-dimensional regularization of chiral gauge theories
Fukaya, Hidenori; Yamamoto, Shota; Yamamura, Ryo
2016-01-01
We propose a non-perturbative regularization of four dimensional chiral gauge theories. In our formulation, we consider a Dirac fermion in six dimensions with two different mass terms having domain-wall profiles in the fifth and the sixth directions, respectively. A Weyl fermion appears as a localized mode at the junction of two different domain-walls. One domain-wall naturally exhibits the Stora-Zumino chain of the anomaly descent equations, starting from the axial U(1) anomaly in six-dimensions to the gauge anomaly in four-dimensions. Another domain-wall mediates a similar inflow of the global anomalies. The anomaly free condition is equivalent to requiring that the axial U(1) anomaly and the parity anomaly are canceled among the six-dimensional Dirac fermions. Since our formulation is a massive vector-like theory, a non-perturbative regularization is possible on a lattice. Putting the gauge field at the four-dimensional junction and extending it to the bulk using the Yang-Mills gradient flow, as recently p...
International Nuclear Information System (INIS)
The fermion in the gauge invariant formulation of the chiral Schwinger model and its relation to the fermion in the anomalous formulation is studied. A gauge invariant fermion operator is constructed that does not give rise to an asymptotic fermion field. It fits in the scheme prepared by generalized Schwinger models. Singularities in the short-distance limit of the chiral Schwinger model in the anomalous formulation lead to the conclusion that it is not a promising starting point for investigations towards realistic (3+1)-dimensional gauge theories with chiral fermion content. A new anomalous (1+1)-dimensional model is studied, the chiral quantum gravity. It is proven to be consistent if only a limited number of chiral fermions couple. The fermion propagator behaves analogously to the one in the massless Thirring model. A general rule is derived for the change of the fermion operator, which is induced by the breakdown of a gauge symmetry. (orig.)
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
International Nuclear Information System (INIS)
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
Supersymmetry, quantum gauge anomalies and generalized Chern-Simons terms in chiral gauge theory
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Torsten
2009-05-13
The purpose of this thesis is to investigate the interplay of anomaly cancellation and generalized Chern-Simons terms in four-dimensional chiral gauge theory. We start with a detailed discussion of generalized Chern-Simons terms with the canellation of anomalies via the Green-Schwarz mechanism. With this at hand, we investigate the situation in general N=1 supersymmetric field theories with generalized Chern-Simons terms. Two simple consistency conditions are shown to encode strong constraints on the allowed anomalies for different types of gauge groups. In one major part of this thesis we are going to display to what extent one has to modify the existing formalism in order to allow for the cancellation of quantum gauge anomalies via the Green-Schwarz mechanism. At the end of this thesis we comment on a puzzle in the literature on supersymmetric field theories with massive tensor fields. The potential contains a term that does not arise from eliminating an auxiliary field. We clarify the origin of this term and display the relation to standard D-term potential. In an appendix it is explicitly shown how these low energy effective actions might be connected to the formulation of four-dimensional gauge theories discussed at earlier stages of this thesis. (orig.)
6d strings from new chiral gauge theories
Kim, Hee-Cheol; Park, Jaemo
2016-01-01
We study the 6d $\\mathcal{N}=(1,0)$ superconformal field theory with smallest non-Higgsable gauge symmetry $SU(3)$. In particular, we propose new 2d gauge theory descriptions of its self-dual strings in the tensor branch. We use our gauge theories to compute the elliptic genera of the self-dual strings, which completely agree with the partial data known from topological strings. We further study the strings of the $(E_6,E_6)$ conformal matter by generalizing our 2d gauge theories. We also show that anomalies of all our gauge theories agree with the self-dual string anomalies computed by inflows from 6d.
Perturbative analysis of the Gauss-law anomaly in chiral gauge theories
International Nuclear Information System (INIS)
We discuss the Gauss-law constraint in chiral gauge theories. A unitarity condition for the Gauss constraint is introduced and shown to be equivalent to the diagrammatic form of the Ward identities. We give a simple derivation of the chiral anomaly and relate it to the breakdown of the unitarity condition
Mathematical Derivation of Chiral Anomaly in Lattice Gauge Theory with Wilson's Action
Hattori, T G; Hattori, Tetsuya; Watanabe, Hiroshi
1998-01-01
Chiral U(1) anomaly is derived with mathematical rigor for a Euclidean fermion coupled to a smooth external U(1) gauge field on an even dimensional torus as a continuum limit of lattice regularized fermion field theory with the Wilson term in the action. The present work rigorously proves for the first time that the Wilson term correctly reproduces the chiral anomaly.
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Machado, F. A.; Natale, A. A.
2011-01-01
We study chiral symmetry breaking in QCD-like gauge theories introducing a confining effective propagator, as proposed recently by Cornwall, and considering the effect of dynamical gauge boson mass generation. The effective confining propagator has the form $1/(k^2+m^2)^2$ and we study the bifurcation equation finding limits on $m$ below which a satisfactory fermion mass solution is generated. Since the coupling constant and gauge boson propagator are damped in the infrared, due to the presen...
The decoupling of right-handed neutrinos in chiral lattice gauge theories
International Nuclear Information System (INIS)
The decoupling of the right-handed fermion in the continuum limit is proved for a class of chiral lattice gauge theories for which the right-handed fermion transforms trivially under the gauge group. No tuning is necessary. The theorem follows from a new fermion shift symmetry. (orig.)
Centre vortices underpin dynamical chiral symmetry breaking in $\\mathrm{SU}(3)$ gauge theory
Trewartha, Daniel; Leinweber, Derek
2015-01-01
The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure $\\mathrm{SU}(3)$ gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smo...
D-brane Instantons as Gauge Instantons in Orientifolds of Chiral Quiver Theories
Franco, Sebastian; Uranga, Angel
2015-01-01
Systems of D3-branes at orientifold singularities can receive non-perturbative D-brane instanton corrections, inducing field theory operators in the 4d effective theory. In certain non-chiral examples, these systems have been realized as the infrared endpoint of a Seiberg duality cascade, in which the D-brane instanton effects arise from strong gauge theory dynamics. We present the first UV duality cascade completion of chiral D3-brane theories, in which the D-brane instantons arise from gauge theory dynamics. Chiral examples are interesting because the instanton fermion zero mode sector is topologically protected, and therefore lead to more robust setups. As an application of our results, we provide a UV completion of certain D-brane orientifold systems recently claimed to produce conformal field theories with conformal invariance broken only by D-brane instantons.
Evidence that centre vortices underpin dynamical chiral symmetry breaking in SU (3) gauge theory
Trewartha, Daniel; Kamleh, Waseem; Leinweber, Derek
2015-07-01
The link between dynamical chiral symmetry breaking and centre vortices in the gauge fields of pure SU (3) gauge theory is studied using the overlap-fermion quark propagator in Lattice QCD. Overlap fermions provide a lattice realisation of chiral symmetry and consequently offer a unique opportunity to explore the interplay of centre vortices, instantons and dynamical mass generation. Simulations are performed on gauge fields featuring the removal of centre vortices, identified through gauge transformations maximising the center of the gauge group. In contrast to previous results using the staggered-fermion action, the overlap-fermion results illustrate a loss of dynamical chiral symmetry breaking coincident with vortex removal. This result is linked to the overlap-fermion's sensitivity to the subtle manner in which instanton degrees of freedom are compromised through the process of centre vortex removal. Backgrounds consisting solely of the identified centre vortices are also investigated. After smoothing the vortex-only gauge fields, we observe dynamical mass generation on the vortex-only backgrounds consistent within errors with the original gauge-field ensemble following the same smoothing. Through visualizations of the instanton-like degrees of freedom in the various gauge-field ensembles, we find evidence of a link between the centre vortex and instanton structure of the vacuum. While vortex removal destabilizes instanton-like objects under O (a4)-improved cooling, vortex-only backgrounds provide gauge-field degrees of freedom sufficient to create instantons upon cooling.
Chiral anomalies in higher-derivative supersymmetric 6D gauge theories
International Nuclear Information System (INIS)
We show that the recently constructed higher-derivative 6D SYM theory involves internal chiral anomaly breaking gauge invariance. The anomaly is cancelled when adding to the theory an adjoint matter hyper-multiplet. One shows that as the effective charge grows at high energies, the theories are not consistently defined nonperturbatively. Constructing a nontrivial 6D theory that would be internally consistent both perturbatively and nonperturbatively remains a major challenge. (author)
A numerical solution to the local cohomology problem in U(1) chiral gauge theories
Kadoh, Daisuke; Kikukawa, Yoshio
2005-01-01
We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincaré lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.
A numerical solution to the local cohomology problem in U(1) chiral gauge theories
Kadoh, D; Kadoh, Daisuke; Kikukawa, Yoshio
2005-01-01
We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties.
A numerical solution to the local cohomology problem in U(1) chiral gauge theories
International Nuclear Information System (INIS)
We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties. (author)
A numerical solution to the local cohomology problem in U(1) chiral gauge theories
Energy Technology Data Exchange (ETDEWEB)
Kadoh, Daisuke; Kikukawa, Yoshio [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)]. E-mail: kikukawa@eken.phys.nagoya-u.ac.jp
2005-01-01
We consider a numerical method to solve the local cohomology problem related to the gauge anomaly cancellation in U(1) chiral gauge theories. In the cohomological analysis of the chiral anomaly, it is required to carry out the differentiation and the integration of the anomaly with respect to the continuous parameter for the interpolation of the admissible gauge fields. In our numerical approach, the differentiation is evaluated explicitly through the rational approximation of the overlap Dirac operator with Zolotarev optimization. The integration is performed with a Gaussian Quadrature formula, which turns out to show rather good convergence. The Poincare lemma is reformulated for the finite lattice and is implemented numerically. We compute the current associated with the cohomologically trivial part of the chiral anomaly in two-dimensions and check its locality properties. (author)
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.
Solving the local cohomology problem in U(1) chiral gauge theories within a finite lattice
Energy Technology Data Exchange (ETDEWEB)
Kadoh, Daisuke; Nakayama, Yoichi; Kikukawa, Yoshio [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan)]. E-mail: kikukawa@eken.phys.nagoya-u.ac.jp
2004-12-01
In the gauge-invariant construction of abelian chiral gauge theories on the lattice based on the Ginsparg-Wilson relation, the gauge anomaly is topological and its cohomologically trivial part plays the role of the local counter term. We give a prescription to solve the local cohomology problem within a finite lattice by reformulating the Poincare lemma so that it holds true on the finite lattice up to exponentially small corrections. We then argue that the path-integral measure of Weyl fermions can be constructed directly from the quantities defined on the finite lattice. (author)
Aoki, Ken-Ichi; Sato, Daisuke
2016-01-01
We analyze the dynamical chiral symmetry breaking in gauge theory with the nonperturbative renormalization group equation (NPRGE), which is a first order nonlinear partial differential equation (PDE). In case that the spontaneous chiral symmetry breaking occurs, the NPRGE encounters some non-analytic singularities at the finite critical scale even though the initial function is continuous and smooth. Therefore there is no usual solution of the PDE beyond the critical scale. In this paper, we newly introduce the notion of a weak solution which is the global solution of the weak NPRGE. We show how to evaluate the physical quantities with the weak solution.
Universality of spontaneous chiral symmetry breaking in gauge theories
International Nuclear Information System (INIS)
We investigate one-flavor QCD with an additional chiral scalar field. For a large domain in the space of coupling constants, this model belongs to the same universality class as QCD, and the effects of the scalar become unobservable. This is connected to a 'bound-state fixed point' of the renormalization flow for which all memory of the microscopic scalar interactions is lost. The QCD domain includes a microscopic scalar potential with minima at a nonzero field. On the other hand, for a scalar mass term m2 below a critical value mc2, the universality class is characterized by perturbative spontaneous chiral symmetry breaking which renders the quarks massive. Our renormalization group analysis shows how this universality class is continuously connected with the QCD universality class
Chiral observables and S-duality in N = 2* U(N) gauge theories
Ashok, S K; Dell'Aquila, E; Frau, M; Lerda, A; Moskovic, M; Raman, M
2016-01-01
We study N = 2* theories with gauge group U(N) and use equivariant localization to calculate the quantum expectation values of the simplest chiral ring elements. These are expressed as an expansion in the mass of the adjoint hypermultiplet, with coefficients given by quasi-modular forms of the S-duality group. Under the action of this group, we construct combinations of chiral ring elements that transform as modular forms of definite weight. As an independent check, we confirm these results by comparing the spectral curves of the associated Hitchin system and the elliptic Calogero-Moser system. We also propose an exact and compact expression for the 1-instanton contribution to the expectation value of the chiral ring elements.
Classifying the Phases of Gauge Theories by Spectral Density of Probing Chiral Quarks
Alexandru, Andrei
2015-01-01
We describe our recent proposal that distinct phases of gauge theories with fundamental quarks translate into specific types of low-energy behavior in Dirac spectral density. The resulting scenario is built around new evidence substantiating the existence of a phase characterized by bimodal (anomalous) density, and corresponding to deconfined dynamics with broken valence chiral symmetry. We argue that such anomalous phase occurs quite generically in these theories, including in "real world" QCD above the crossover temperature, and in zero-temperature systems with many light flavors.
Global Currents, Phase Transitions, and Chiral Symmetry Breaking in Large N_c Gauge Theory
Albash, T; Johnson, C V; Kundu, A; Albash, Tameem; Filev, Veselin; Johnson, Clifford V.; Kundu, Arnab
2006-01-01
We study the finite temperature dynamics of SU(N_c) gauge theory for large N_c, with fundamental quark flavours in a quenched approximation, in the presence of a fixed charge under a global current. We observe several notable phenomena. There is a first order phase transition where the quark condensate jumps discontinuously at finite quark mass, generalizing similar transitions seen at zero charge. We find a non-zero condensate at zero quark mass above a critical value of the charge, corresponding to an analogue of spontaneous chiral symmetry breaking at finite number density. We find that the spectrum of mesons contains the expected associated Goldstone (``pion'') degrees of freedom with a mass dependence on the quark mass that is consistent with the Gell-Mann-Oakes-Renner relation. Our tool in these studies is holography, the string dual of the gauge theory being the geometry of $N_c$ spinning D3-branes at finite temperature, probed by a D7-brane.
Shi, Yan-Liang
2015-01-01
We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{\\bar A_\\ell}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\\ell$ tensor representation, $\\bar A_\\ell$, of this group with $k, \\ \\ell \\ge 2$. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with $k=\\ell=2$ in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry brea...
Features of a 2d Gauge Theory with Vanishing Chiral Condensate
Landa-Marbán, David; Bietenholz, Wolfgang; Hip, Ivan
2013-01-01
The Schwinger model with $N_f \\geq 2$ flavors is a simple example for a fermionic model with zero chiral condensate Sigma (in the chiral limit). We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward in the recent literature for models with Sigma = 0, which include IR conformal theories. In particular we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mas...
On gravitational dressing of 2D field theories in chiral gauge
International Nuclear Information System (INIS)
After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no explicit gravitational dressing factor, analogue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the gravitationally dressed four-point correlation function of products of left and right fermions. We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the power-law singularity in the absence of gravity. This rather surprising effect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansions. We also discuss some perturbative evidence that the chiral Gross-Neveu model may remain integrable when coupled to gravity. (orig.)
Microscopic Dirac Spectrum in a 2d Gauge Theory with Zero Chiral Condensate
Bietenholz, Wolfgang; Hip, Ivan; Landa-Marbán, David
2013-01-01
Fermionic theories with a vanishing chiral condensate (in the chiral limit) have recently attracted considerable interest; in particular variants of multi-flavour QCD are candidates for this behaviour. Here we consider the 2-flavour Schwinger model as a simple theory with this property. Based on simulations with light dynamical overlap fermions, we test the hypothesis that in such models the low lying Dirac eigenvalues could be decorrelated. That has been observed in 4d Yang-Mills theories at...
Wen, Xiao-Gang
2013-01-01
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of the standard model as a Hamiltonian quantum mechanical theory. Here we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non...
Wen, Xiao-Gang
2013-01-01
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of standard model as a Hamiltonian quantum mechanical theory. In this paper, we propose a way to give a modified standard model (with 48 two-component Weyl fermions)...
Electric/magnetic duality for chiral gauge theories with anomaly cancellation
De Rydt, Jan; Schmidt, Torsten T.; Trigiante, Mario; Proeyen, Antoine; Zagermann, Marco
2008-01-01
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes previous work on the symplectically covariant formulation of anomaly-free gauge theories as they typically occur in extended supergravity, and now also includes general theories with (pseudo-)anomalous gauge interactions as they may occur in global or local...
Microscopic Dirac Spectrum in a 2d Gauge Theory with Zero Chiral Condensate
Bietenholz, Wolfgang; Landa-Marbán, David
2013-01-01
Fermionic theories with a vanishing chiral condensate (in the chiral limit) have recently attracted considerable interest; in particular variants of multi-flavour QCD are candidates for this behaviour. Here we consider the 2-flavour Schwinger model as a simple theory with this property. Based on simulations with light dynamical overlap fermions, we test the hypothesis that in such models the low lying Dirac eigenvalues could be decorrelated. That has been observed in 4d Yang-Mills theories at high temperature, but it cannot be confirmed for the 2-flavour Schwinger model. We also discuss subtleties in the evaluation of the mass anomalous dimension and its IR extrapolation.
International Nuclear Information System (INIS)
An introduction to the unified gauge theories of weak and electromagnetic interactions is given. The ingredients of gauge theories and symmetries and conservation laws lead to discussion of local gauge invariance and QED, followed by weak interactions and quantum flavor dynamics. The construction of the standard SU(2)xU(1) model precedes discussion of the unification of weak and electromagnetic interactions and weak neutral current couplings in this model. Presentation of spontaneous symmetry breaking and spontaneous breaking of a local symmetry leads to a spontaneous breaking scheme for the standard SU(2)xU(1) model. Consideration of quarks, leptons, masses and the Cabibbo angles, of the four quark and six quark models and CP violation lead finally to grand unification, followed by discussion of mixing angles in the Georgi-Glashow model, the Higgses of the SU(5) model and proton/ neutron decay in SU(5). (JIW)
Chiral symmetry breaking in asymptotically free and non-asymptotically free gauge theories
International Nuclear Information System (INIS)
An essential distinction in the realization of the PCAC-dynamics in vector-like asymptotically free and non-asymptotically free (with a non-trival ultraviolet stable fixed point) gauge theories is revealed. For the latter theories an analytical expression for the condensate is obtained in the two-loop approximation and the arguments in support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed
Fast algorithms for simulating chiral fermions in U(1)lattice gauge theory
Xhako, Dafina
2014-01-01
In order to develop fast inversion algorithms we have used overlap solvers in two dimensions. Lattice QED theory with U(1) group symmetry in two dimensional space-times dimensions has always been a testing ground for algorithms. By the other side, motivated by our previews work that the two-grid algorithm converge faster than the standard iterative methods for overlap inversion but not for all quark masses, we thought to test this idea in less dimensions such as U(1) gauge theory. Our main objective of this paper it is to implement and develop the idea of a two level algorithm in a new algorithm coded in QCDLAB. This implementation is presented in the preconditioned GMRESR algorithm, as our new contribution in QCDLAB package. The preconditioned part of our algorithm, different from the one of [18], is the approximation of the overlap operator with the truncated overlap operator with finite N3 dimension. We have tested it for 100 statistically independent configurations on 32 x 32 lattice background U(1) field...
Deconfinement and chiral symmetry restoration in an SU(3) gauge theory with adjoint fermions
International Nuclear Information System (INIS)
We analyze the finite temperature phase diagram of QCD with fermions in the adjoint representation. The simulations performed with four dynamical Majorana fermions show that the deconfinement and chiral phase transitions occur at two distinct temperatures. While the deconfinement transition is first-order at Td we find evidence for a continuous chiral transition at a higher temperature Tc ≅ 8 Td. We observe a rapid change of bulk thermodynamic observables at Td which reflects the increase in the number of degrees of freedom. However, these show little variation at Tc, where the fermion condensate vanishes. We also analyze the potential between static fundamental and adjoint charges in all three phases and extract the corresponding screening masses above Td
Introduction to gauge theories
International Nuclear Information System (INIS)
In these lectures we present the key ingredients of theories with local gauge invariance. We introduce gauge invariance as a starting point for the construction of a certain class of field theories, both for abelian and nonabelian gauge groups. General implications of gauge invariance are discussed, and we outline in detail how gauge fields can acquire masses in a spontaneous fashion. (orig./HSI)
Lattice gauge theory: Present status
International Nuclear Information System (INIS)
Lattice gauge theory is our primary tool for the study of non- perturbative phenomena in hadronic physics. In addition to giving quantitative information on confinement, the approach is yielding first principles calculations of hadronic spectra and matrix elements. After years of confusion, there has been significant recent progress in understanding issues of chiral symmetry on the lattice
Chiral magnetic effect by synthetic gauge fields
Hayata, Tomoya
2016-01-01
We study the dynamical generation of the chiral chemical potential in a Weyl metal constructed from a three-dimensional optical lattice and subject to synthetic gauge fields. By numerically solving the Boltzmann equation with the Berry curvature in the presence of parallel synthetic electric and magnetic fields, we find that the spectral flow and the ensuing chiral magnetic current emerge. We show that the spectral flow and the chiral chemical potential can be probed by time-of-flight imaging.
Wu, Ning
1998-01-01
In this paper, we will construct a gauge field model, in which the masses of gauge fields are non-zero and the local gauge symmetry is strictly preserved. A SU(N) gauge field model is discussed in details in this paper. In the limit $\\alpha \\longrightarrow 0$ or $\\alpha \\longrightarrow \\infty$, the gauge field model discussed in this paper will return to Yang-Mills gauge field model. This theory could be regarded as theoretical development of Yang-Mills gauge field theory.
Torons, chiral symmetry breaking and U(1) problem in σ-model and gauge theories. Part 2
International Nuclear Information System (INIS)
The main point of this work is the physical consenquences of the existence of fractional charge in the σ-models and espesially in the physically interesting theory QCD. It is shown that the corresponding fluctuations ensure spontaneous breaking of the chiral symmetry and give a nonzero contribution to the chiral condensate. Toron solution is determined on the manifold with boundary. In this case many questions arise such as: global boundary conditions, the stability of the solution, self-adjointness of Dirac operator, single-valuedness of the physical values and so on. These questions are interconnected and turn out to be self cobsistent only for the special choice of the topological number (Q=1/2 for SU(2)). It is shown that in the Dirac's spectrum of the quarks the gap between zero and the continuum is absent. 50 refs.; 10 figs
International Nuclear Information System (INIS)
An essential distinction in the relaization of the PCAC dynamics in asymptotically free and non-asymptotically free (with a non-trivial ultraviolet-stable fixed point) gauge theories is revealed. For the latter theories an analytical expressions for the condensate is obtained in the two-loop approximation and arguments of support of a soft behaviour at small distances of composite operators are given. The problem of factorizing the low-energy region for the Wess-Zumino-Witten action is discussed. Besides, the mass relations for pseudoscalar mesons in arbitrary Θ-sector are obtained in the first order in fermion bare masses and the impossibility for spontaneous P and CP-symmetries breaking in vector-like gauge theories at Θ=0 is shown
Supersymmetric Gauge Theories from String Theory
Metzger, Steffen
2005-01-01
The subject of this thesis are 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 subcycles. Properties of the gauge theory are then mapped to the geometric structure of the Calabi-Yau space. In particular, the low energy effective superpotential...
Study of gauge symmetry of both the free and gauged chiral boson through the Lagrangian formulation
International Nuclear Information System (INIS)
Every basic interaction is supposed to have their origin from the gauge principle and understanding of the gauge symmetry of a physical theory is a very important problem which has received much attention to the physicist from the long past. Their exists some transformation that leaves physical contents of the gauge theory invariant. It even stands as a fundamental principle that determines the form of Lagrangian of a theory. Two main approaches have been followed in the literature to study the local gauge symmetry of a given Lagrangian. The oldest one is the Hamiltonian formulation based on Dirac conjecture. It is true that unitarity of a theory can not be well understood without Hamiltonian approach. However it does not always lead to Lorentz covariant generating functional. This drawback indeed has the remedy in the Lagrangian formulation. The gauge symmetry related studies on dynamical theory should therefore be extended with equal intensities in both the formalism. It would certainly be of interest to find out the appropriate gauge transformation of different theories using the Lagrangian formulation. It would be much more interesting to extend this formulation in the extended phase space needed to restore the gauge invariance. Chiral boson which is considered as the basic ingredient of heterotic string is a rich theoretical model. Gauged chiral boson is also interesting in many respects. So we have studied the gauge property of free and gauged chiral boson both in the usual phase space and in the extended phase space and found that the formulation works in the manner like the Hamiltonian formulation. (author)
De Castro, A S
1999-01-01
A canonical action describing the interaction of chiral gauge fields in D=6 Minkowski space-time is constructed. In a particular partial gauge fixing it reduces to the action found by Perry and Schwarz. The additional gauge symmetries are used to show the off-shell equivalence of the dimensional reduction to D=5 Minkowski space-time of the chiral gauge field canonical action and the Born-Infeld canonical action describing an interacting D=5 Abelian vector field. Its extension to improve the on-shell equivalence arguments of dual D-brane actions to off-shell ones is discussed.
Supergravity from Gauge Theory
Berkowitz, Evan
2016-01-01
Gauge/gravity duality is the conjecture that string theories have dual descriptions as gauge theories. Weakly-coupled gravity is dual to strongly-coupled gauge theories, ideal for lattice calculations. I will show precision lattice calculations that confirm large-N continuum D0-brane quantum mechanics correctly reproduces the leading-order supergravity prediction for a black hole's internal energy---the first leading-order test of the duality---and constrains stringy corrections.
Anomaly cancellation condition in lattice gauge theory
International Nuclear Information System (INIS)
We show that, to all orders of powers of the gauge potential, a gauge anomaly Α defined on 4-dimensional infinite lattice can always be removed by a local counterterm, provided that Α depends smoothly and locally on the gauge potential and that Α reproduces the gauge anomaly in the continuum theory in the classical continuum limit: The unique exception is proportional to the anomaly in the continuum theory. This follows from an analysis of nontrivial local solutions to the Wess-Zumino consistency condition in lattice gauge theory. Our result is applicable to the lattice chiral gauge theory based on the Ginsparg-Wilson Dirac operator, when the gauge field is sufficiently weak parallel-U(n,μ) - 1-parallel < ε', where U(n,μ) is the link variable and ε' a certain small positive constant. (author)
Gauge-fixing Condition on Generating Superfield of Chiral Multiplet
Kimura, Tetsuji
2015-01-01
We study a supergauge transformation of a complex superfield which generates a chiral superfield in two-dimensional ${\\cal N}=(2,2)$ theory. We refer to this complex superfield as the generating superfield. The chiral superfield is not sensitive of the supergauge transformation. Since there exist redundant component fields in the generating superfield, we remove some of them by a gauge-fixing condition. This situation is parallel to that of a vector superfield. In order to obtain a suitable configuration of the GLSM for the exotic five-brane which gives rise to a nongeometric background, we impose a relatively relaxed gauge-fixing condition. It turns out that the gauge-fixed generating superfield is different from a semichiral superfield whose scalar field represents a coordinate of generalized K\\"{a}hler geometry.
International Nuclear Information System (INIS)
After a general introduction to the structure of effective field theories, the main ingredients of chiral perturbation theory are reviewed. Applications include the light quark mass ratios and pion-pion scattering to two-loop accuracy. In the pion-nucleon system, the linear σ model is contrasted with chiral perturbation theory. The heavy-nucleon expansion is used to construct the effective pion-nucleon Lagrangian to third order in the low-energy expansion, with applications to nucleon Compton scattering. (author)
Supersymmetric N=2 gauge theory with arbitrary gauge group
Kuchiev, Michael
2009-01-01
A universal model, which implements the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It has a clear form based on the hyperelliptic curve, whose genus equals the rank of the gauge group. The weak and strong coupling limits are reproduced correctly. The magnetic and electric charges of light dyons, which are present in the proposed model at strong coupling comply with recent predictions derived from the general properties of N=2 and N=1 gauge theories. The discrete chiral symmetry is implemented, the duality condition is reproduced, and connections between monodromies at weak and strong coupling are established. The model predicts the identical analytic structure of the coupling constants for the theories based on the SU(r+1) and Sp(2r) gauge groups.
Chung, Daniel J H
2016-01-01
We reformulate gauge theories in analogy with the vierbein formalism of general relativity. More specifically, we reformulate gauge theories such that their gauge dynamical degrees of freedom are local fields that transform linearly under the dual representation of the charged matter field. These local fields, which naively have the interpretation of non-local operators similar to Wilson lines, satisfy constraint equations. A set of basis tensor fields are used to solve these constraint equations, and their field theory is constructed. A new local symmetry in terms of the basis tensor fields is used to make this field theory local and maintain a Hamiltonian that is bounded from below. The field theory of the basis tensor fields is what we call the basis tensor gauge theory.
Baryon chiral perturbation theory
International Nuclear Information System (INIS)
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order O(q6) and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Baryon chiral perturbation theory
Scherer, Stefan
2011-01-01
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order ${\\cal O}(q^6)$ and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Baryon chiral perturbation theory
Scherer, S.
2012-03-01
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order Script O(q6) and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Maas, Axel
2012-01-01
QCD can be formulated using any gauge group. One particular interesting choice is to replace SU(3) by the exceptional group G2. Conceptually, this group is the simplest group with a trivial center. It thus permits to study the conjectured relevance of center degrees of freedom for QCD. Practically, since all its representation are real, it is possible to perform lattice simulations for this theory also at finite baryon densities. It is thus an excellent environment to test methods and to investigate general properties of gauge theories at finite densities. We review the status of our understanding of gauge theories with the gauge group G2, including Yang-Mills theory, Yang-Mills-Higgs theory, and QCD both in the vacuum and in the phase diagram.
Radiative meson decays in chiral perturbation theory
International Nuclear Information System (INIS)
Radiative meson decays are a fertile field for chiral perturbation theory. Chiral symmetry together with gauge invariance yield stringent constraints on radiative decay amplitudes. In addition to predicting decay rates and spectra, the chiral approach allows for a unified description of CP violation in radiative K decays. The chiral viewpoint in the recent controversy over the magnitude of two-photon exchange in the decay KL→ π0e+e- is exposed. The radiative decay η→π0γγ is discussed as an intriguing case where the leading result of chiral perturbation theory seems to be too small by two orders of magnitude in rate. 32 refs., 3 figs. (Author)
International Nuclear Information System (INIS)
Assuming that a lattice gauge theory describes a fundamental attribute of Nature, it should be pointed out that such a theory in the form of a gauge glass is a weaker assumption than a regular lattice model in as much as it is not constrained by the imposition of translational invariance; translational invariance is, however, recovered approximately in the long wavelength or continuum limit. (orig./WL)
Supersymmetric gauge theories from string theory
International Nuclear Information System (INIS)
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 G2-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 G2-manifold is known. Here we construct families of metrics on compact weak G2-manifolds, which contain two conical singularities. Weak G2-manifolds have properties that are similar to the ones of proper G2-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 E8 x E8-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 classical action. (author)
Sobreiro, R. F.; Tomaz, A. A.; Otoya, V. J. Vasquez
2012-01-01
Pure gauge theories for de Sitter, anti de Sitter and orthogonal groups, in four-dimensional Euclidean spacetime, are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective geometry may be induced and a gravity theory emerges.
International Nuclear Information System (INIS)
In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed
Digital lattice gauge theories
Zohar, Erez; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a $\\mathbb{Z}_{3}$ lattice gauge theory with dynamical fermionic matter in $2+1$ dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms...
International Nuclear Information System (INIS)
This chapter attempts to present some of the fundamental geometrical ideas at the basis of gauge theories. Describes Dirac Monopoles and discusses those ideas that are not usually found in more ''utilitarian'' presentations which concentrate on QCD or on the Glashow-Salam-Weinberg model. This topic was chosen because of the announcement of the possible detection of a Dirac monopole. The existence of monopoles depends on topological features of gauge theories (i.e., on global properties of field configurations which are unique to gauge theories). Discusses global symmetry-local symmetry; the connection; path dependence and the gauge fields; topology and monopoles; the case of SU(3) x U(1); and the 't Hooft-Polyakov monopole
International Nuclear Information System (INIS)
One of the most fundamental questions we can ask about a given gauge theory is its phase diagram. In the Standard Model, we observe three fundamentally different types of behavior: QCD is in a confined phase at zero temperature, while the electroweak sector of the Standard Model combines Coulomb and Higgs phases. Our current understanding of the phase structure of gauge theories owes much to the modern theory of phase transitions and critical phenomena, but has developed into a subject of extensive study. After reviewing some fundamental concepts of phase transitions and finite-temperature gauge theories, we discuss some recent work that broadly extends our knowledge of the mechanisms that determine the phase structure of gauge theories. A new class of models with a rich phase structure has been discovered, generalizing our understanding of the confinement–deconfinement transition in finite-temperature gauge theories. Models in this class have spacetime topologies with one or more compact directions. On R3 × S1, the addition of double-trace deformations or periodic adjoint fermions to a gauge theory can yield a confined phase in the region where the S1 circumference L is small, so that the coupling constant is small, and semiclassical methods are applicable. In this region, Euclidean monopole solutions, which are constituents of finite-temperature instantons, play a crucial role in the calculation of a non-perturbative string tension. We review the techniques used to analyze this new class of models and the results obtained so far, as well as their application to finite-temperature phase structure, conformal phases of gauge theories and the large-N limit. (topical review)
Blagojević, Milutin
2012-01-01
During the last five decades, gravity, as one of the fundamental forces of nature, has been formulated as a gauge field theory of the Weyl-Cartan-Yang-Mills type. The resulting theory, the Poincar\\'e gauge theory of gravity, encompasses Einstein's gravitational theory as well as the teleparallel theory of gravity as subcases. In general, the spacetime structure is enriched by Cartan's torsion and the new theory can accommodate fermionic matter and its spin in a perfectly natural way. The present reprint volume contains articles from the most prominent proponents of the theory and is supplemented by detailed commentaries of the editors. This guided tour starts from special relativity and leads, in its first part, to general relativity and its gauge type extensions a la Weyl and Cartan. Subsequent stopping points are the theories of Yang-Mills and Utiyama and, as a particular vantage point, the theory of Sciama and Kibble. Later, the Poincar\\'e gauge theory and its generalizations are explored and specific topi...
Topological Summation in Lattice Gauge Theory
Bietenholz, Wolfgang; Hip, Ivan
2012-01-01
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a model is simulated with local updates of the lattice gauge configuration, the Monte Carlo history tends to get stuck in one sector for many steps, in particular on fine lattices. Then expectation values can be measured only within specific sectors. Here we p...
Investigation of gauge-fixed pure U(1) theory at strong coupling
Basak, S; De, Asit K.
2002-01-01
We numerically investigate the phase diagram of pure U(1) gauge theory with gauge fixing at strong gauge coupling. The FM-FMD phase transition, which proved useful in defining Abelian lattice chiral gauge theory, persists also at strong gauge coupling. However, there the transition seems no to be longer continuous. At large gauge couplings we find evidences for confinement.
Investigation of gauge-fixed pure U(1) theory at strong coupling
International Nuclear Information System (INIS)
We numerically investigate the phase diagram of pure U(1) gauge theory with gauge fixing at strong gauge coupling. The FM-FMD phase transition, which proved useful in defining Abelian lattice chiral gauge theory, persists also at strong gauge coupling. However, there the transition seems no longer to be continuous. At large gauge couplings we find evidences for confinement
Spontaneous symmetry breakdown in gauge theories
International Nuclear Information System (INIS)
The dynamical theory of spontaneous breakdown correctly predicts the bound states and relates the order parameters of electron-photon superconductivity and quark-gluon chiral symmetry. A similar statement cannot be made for the standard electro-weak gauge symmetry. (author)
International Nuclear Information System (INIS)
We analyze the behaviour that correlation functions ought to have on the lattice in order to reproduce QCD sum rules in the continuum limit. We formulate a set of relations between lattice correlation functions of meson operators at small time separation and the quark condensates responsible for spontaneous breakdown of chiral symmetry. We suggest that the degree to which such relations are satisfied will provide a set of consistency checks on the ability of lattice Monte Carlo simulations to reproduce the correct spontaneous chiral symmetry breaking of the continuum limit. (author)
Bais, F A
1995-01-01
In these lecture notes, we present a self-contained discussion of planar gauge theories broken down to some finite residual gauge group H via the Higgs mechanism. The main focus is on the discrete H gauge theory describing the long distance physics of such a model. The spectrum features global H charges, magnetic vortices and dyonic combinations. Due to the Aharonov-Bohm effect, these particles exhibit topological interactions. Among other things, we review the Hopf algebra related to this discrete H gauge theory, which provides an unified description of the spin, braid and fusion properties of the particles in this model. Exotic phenomena such as flux metamorphosis, Alice fluxes, Cheshire charge, (non)abelian braid statistics, the generalized spin-statistics connection and nonabelian Aharonov-Bohm scattering are explained and illustrated by representative examples. Preface: Broken symmetry revisited, 1 Basics: 1.1 Introduction, 1.2 Braid groups, 1.3 Z_N gauge theory, 1.3.1 Coulomb screening, 1.3.2 Survival o...
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
International Nuclear Information System (INIS)
This lecture is devoted to the discussion of gauge field theory permitting from the single point of view to describe all the interactions of elementary particles. The authors used electrodynamics and the Einstein theory of gravity to search for a renormgroup fixing a form of Lagrangian. It is shown that the gauge invariance added with the requirement of the minimum number of arbitraries in Lagrangian fixes unambigously the form of the electromagnetic interaction. The generalization of this construction for more complicate charge spaces results in the Yang-Mills theory. The interaction form in this theory is fixed with the relativity principle in the charge space. A quantum scheme of the Yang-Mills fields through the explicit separation of true dynamic variables is suggested. A comfortable relativistically invariant diagram technique for the calculation of a producing potential for the Green functions is described. The Ward generalized identities have been obtained and a procedure of the elimination of ultraviolet and infrared divergencies has been accomplished. Within the framework of QCD (quantum-chromodynamic) the phenomenon of the asymptotic freedom being the most successful prediction of the gauge theory of strong interactions was described. Working methods with QCD outside the framework of the perturbation theory have been described from a coupling constant. QCD is represented as a single theory possessing both the asymptotical freedom and the freedom retaining quarks
Confining gauge theories without Goldstone bosons
International Nuclear Information System (INIS)
We discuss the possibility that in the Wilson lattice definition of confining gauge theories without Goldstone bosons one may systematically adjust the lightest vector mass to zero while keeping the isosinglet scalar mass, which arises by the chiral anomaly, nontachyonic. We discuss a Weyl fermion theory and find the lightest vector particle to be an isoscalar (at least in strong coupling) so that there is no collision with known theorems. We discuss how an abelian gauge symmetry can arise as an infrared attractor and point out a difference between the Weyl fermion theory and one flavour QCD. Attention is also drawn to a physical motivation. (orig.)
Geometrical formulation of gauge theories
International Nuclear Information System (INIS)
We review some basic aspects of the geometry of gauge theories. Particularly, we introduce the concepts gauge potential, field intensity, matter field, gauge groups and symmetry of a physical configuration and we discuss the spontaneous symmetry breaking and the gauge theories of gravitation. 26 refs
Introduction to gauge theories
Maiani, Luciano
2016-01-01
Written by three of the world's leading experts on particle physics and the standard model, including an award-winning former director general of CERN, this book provides a completely up-to-date account of gauge theories. Starting from Feynman’s path integrals, Feynman rules are derived, gauge fixing and Faddeev-Popov ghosts are discussed, and renormalization group equations are derived. Several important applications to quantum electrodynamics and quantum chromodynamics (QCD) are discussed, including the one-loop derivation of asymptotic freedom for QCD.
Gauge Theory by canonical Transformations
Koenigstein, Adrian; Stoecker, Horst; Struckmeier, Juergen; Vasak, David; Hanauske, Matthias
2016-01-01
Electromagnetism, the strong and the weak interaction are commonly formulated as gauge theories in a Lagrangian description. In this paper we present an alternative formal derivation of U(1)-gauge theory in a manifestly covariant Hamilton formalism. We make use of canonical transformations as our guiding tool to formalize the gauging procedure. The introduction of the gauge field, its transformation behaviour and a dynamical gauge field Lagrangian/Hamiltonian are unavoidable consequences of this formalism, whereas the form of the free gauge Lagrangian/Hamiltonian depends on the selection of the gauge dependence of the canonically conjugate gauge fields.
Chiral Flavor Violation from Extended Gauge Mediation
Evans, Jared A; Thalapillil, Arun
2015-01-01
Models of extended gauge mediation, in which large A-terms arise through direct messenger-MSSM superpotential couplings, are well-motivated by the discovery of the 125 GeV Higgs. However, since these models are not necessarily MFV, the flavor constraints could be stringent. In this paper, we perform the first detailed and quantitative study of the flavor violation in these models. To facilitate our study, we introduce a new tool called FormFlavor for computing precision flavor observables in the general MSSM. We validate FormFlavor and our qualitative understanding of the flavor violation in these models by comparing against analytical expressions. Despite being non-MFV, we show that these models are protected against the strongest constraints by a special flavor texture, which we dub chiral flavor violation ($\\chi$FV). This results in only mild bounds from current experiments, and exciting prospects for experiments in the near future.
Chiral flavor violation from extended gauge mediation
Evans, Jared A.; Shih, David; Thalapillil, Arun
2015-07-01
Models of extended gauge mediation, in which large A-terms arise through direct messenger-MSSM superpotential couplings, are well-motivated by the discovery of the 125 GeV Higgs. However, since these models are not necessarily MFV, the flavor constraints could be stringent. In this paper, we perform the first detailed and quantitative study of the flavor violation in these models. To facilitate our study, we introduce a new tool called FormFlavor for computing precision flavor observables in the general MSSM. We validate FormFlavor and our qualitative understanding of the flavor violation in these models by comparing against analytical expressions. Despite being non-MFV, we show that these models are protected against the strongest constraints by a special flavor texture, which we dub chiral flavor violation (χFV). This results in only mild bounds from current experiments, and exciting prospects for experiments in the near future.
Dielectric lattice gauge theory
International Nuclear Information System (INIS)
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
DEFF Research Database (Denmark)
Mojaza, Matin; Pica, Claudio; Sannino, Francesco
2010-01-01
We compute the nonzero temperature free energy up to the order g^6 \\ln(1/g) in the coupling constant for vector like SU(N) gauge theories featuring matter transforming according to different representations of the underlying gauge group. The number of matter fields, i.e. flavors, is arranged in...... such a way that the theory develops a perturbative stable infrared fixed point at zero temperature. Due to large distance conformality we trade the coupling constant with its fixed point value and define a reduced free energy which depends only on the number of flavors, colors and matter representation....... We show that the reduced free energy changes sign, at the second, fifth and sixth order in the coupling, when decreasing the number of flavors from the upper end of the conformal window. If the change in sign is interpreted as signal of an instability of the system then we infer a critical number of...
International Nuclear Information System (INIS)
Lattice gauge theory is now ten years old. Apart from the theoretical insight the lattice formulation gives, it is very well suited for computer simulations, as its inventor advocated already some five years ago at this school. Since three years this approach has extracted useful information out of lattice gauge theory and spurred many interesting questions. In the first lecture, I will assume there are no experts in the audience and explain some basic facts in quarkless quantumchromodynamics on a lattice (QCD). Then, in the second lecture, we shall review tests for the consistency of the numerical results so far obtained. The third lecture shall deal with a more esoteric subject: that of large N reduced models. The list of references is by no means meant to be exhaustive; for that the reader is referred to ref. 27
Emerging Potentials in Higher-Derivative Gauged Chiral Models Coupled to N=1 Supergravity
Farakos, Fotis
2012-01-01
We present a new method to introduce scalar potentials to gauge-invariant chiral models coupled to supergravity. The theories under consideration contain consistent higher-derivative terms which do not give rise to instabilities and ghost states. The chiral auxiliaries are not propagating and can be integrated out. Their elimination gives rise to emerging potentials even when there is not a superpotential to start with. We present the case of a single chiral multiplet with and without a superpotential and, in the gauged theory, up to two chiral multiplets coupled to supergravity with no superpotential. A general feature of the emergent potential is that it is negative defined leading to anti-de Sitter vacua. In the gauge models, competing D-terms may lift the potential leading to stable and metastable de Sitter and Minkowski vacua as well with spontaneously broken supersymmetry.
Digital lattice gauge theories
Zohar, Erez(Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748, Garching, Germany); Farace, Alessandro; Reznik, Benni; Cirac, J Ignacio
2016-01-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with $2+1$ dimensions and higher, are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through pertubative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards exp...
International Nuclear Information System (INIS)
The thermodynamics of gauge theories such as QED and QCD are slightly more complicated than that of theories such as scalar field theory or free fremion field theory. We shall consider QED in some detail in this lecture, and shall generalize the results we find to more complicated gauge theories such as QCD. The results of this analysis are easily generalized to non-abelian gauge theories with scalar fields and spontaneous symmetry breaking such as GUTS
Investigations in gauge theories, topological solitons and string theories
International Nuclear Information System (INIS)
This is the Final Report on a supported research project on theoretical particle physics entitled ''Investigations in Gauge Theories, Topological Solitons and String Theories.'' The major theme of particle theory pursued has been within the rubric of the standard model, particularly on the interplay between symmetries and dynamics. Thus, the research has been carried out primarily in the context of gauge with or without chiral fermions and in effective chiral lagrangian field theories. The topics studied include the physical implications of abelian and non-abelian anomalies on the spectrum and possible dynamical symmetry breaking in a wide range of theories. A wide range of techniques of group theory, differential geometry and function theory have been applied to probe topological and conformal properties of quantum field theories in two and higher dimensions, the breaking of global chiral symmetries by vector-like gauge theories such as QCD,the phenomenology of a possibly strongly interacting Higgs sector within the minimal standard model, and the relevance of solitonic ideas to non-perturbative phenomena at SSC energies
One-loop Chiral Perturbation Theory with two fermion representations
DeGrand, Thomas; Neil, Ethan T; Shamir, Yigal
2016-01-01
We develop Chiral Perturbation Theory for chirally broken theories with fermions in two different representations of the gauge group. Any such theory has a non-anomalous singlet $U(1)_A$ symmetry, yielding an additional Nambu-Goldstone boson when spontaneously broken. We calculate the next-to-leading order corrections for the pseudoscalar masses and decay constants, which include the singlet Nambu-Goldstone boson, as well as for the two condensates. The results can be generalized to more than two representations.
Review of chiral perturbation theory
Indian Academy of Sciences (India)
B Ananthanarayan
2003-11-01
A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented. Some interesting topics with scope for further elaboration are touched upon.
CP violation in gauge theories
Einhorn, Martin B; Wudka, Jose
2000-01-01
We define the CP transformation properties of scalars, fermions and vectors in a gauge theory and show that only three types of interactions can lead to CP violation: scalar interactions, fermion-scalar interactions and $ F \\tilde F $ associated with the strong CP problem and which involve only the gauge fields. For technicolor theories this implies the absence of CP violation within perturbation theory.
Perturbative chiral violations for domain-wall QCD with improved gauge actions
International Nuclear Information System (INIS)
We investigate, in the framework of perturbation theory at finite Ns, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained
International Nuclear Information System (INIS)
The relatively simple Fibre-Bundle geometry of a Yang-Mills gauge theory - mainly the clear distinction between base and fibre - made it possible, between 1953 and 1971, to construct a fully quantized version and prove that theory's renormalizability; moreover, nonperturbative (topological) solutions were subsequently found in both the fully symmetric and the spontaneously broken modes (instantons, monopoles). Though originally constructed as a model formalism, it became in 1974 the mathematical mold holding the entire Standard Model (i.e. QCD and the Electroweak theory). On the other hand, between 1974 and 1984, Einstein's theory was shown to be perturbatively nonrenormalizable. Since 1974, the search for Quantum Gravity has therefore provided the main motivation for the construction of Gauge Theories of Gravity. Earlier, however, in 1958-76 several such attempts were initiated, for aesthetic or heuristic reasons, to provide a better understanding of the algebraic structure of GR. A third motivation has come from the interest in Unification, making it necessary to bring GR into a form compatible with an enlargement of the Standard Model. Models can be classified according to the relevant structure group in the fibre. Within the Poincare group, this has been either the R4 translations, or the Lorentz group SL(2, C) - or the entire Poincare SL(2, C) x R4. Enlarging the group has involved the use of the Conformal SU(2, 2), the special Affine SA(4, R) = SL(4, R) x R4 or Affine A(4, R) groups. Supergroups have included supersymmetry, i.e. the graded-Poincare group (n =1...8 m its extensions) or the superconformal SU(2, 2/n). These supergravity theories have exploited the lessons of the aesthetic-heuristic models - Einstein-Cartan etc. - and also achieved the Unification target. Although perturbative renormalizability has been achieved in some models, whether they satisfy unitarity is not known. The nonperturbative Ashtekar program has exploited the understanding of
Methods of Contemporary Gauge Theory
Makeenko, Yuri
2005-11-01
Preface; Part I. Path Integrals: 1. Operator calculus; 2. Second quantization; 3. Quantum anomalies from path integral; 4. Instantons in quantum mechanics; Part II. Lattice Gauge Theories: 5. Observables in gauge theories; 6. Gauge fields on a lattice; 7. Lattice methods; 8. Fermions on a lattice; 9. Finite temperatures; Part III. 1/N Expansion: 10. O(N) vector models; 11. Multicolor QCD; 12. QCD in loop space; 13. Matrix models; Part IV. Reduced Models: 14. Eguchi-Kawai model; 15. Twisted reduced models; 16. Non-commutative gauge theories.
Stochastic quantization and gauge theories
International Nuclear Information System (INIS)
Stochastic quantization is presented taking the Flutuation-Dissipation Theorem as a guide. It is shown that the original approach of Parisi and Wu to gauge theories fails to give the right results to gauge invariant quantities when dimensional regularization is used. Although there is a simple solution in an abelian theory, in the non-abelian case it is probably necessary to start from a BRST invariant action instead of a gauge invariant one. Stochastic regularizations are also discussed. (author)
Quantization of Galilean gauge theories
International Nuclear Information System (INIS)
Galilean gauge theories are quantized using Dirac's theory of canonical quantization of constrained systems. The infra-red sector for the Abelian case is exactly solved and shown to be analogous to that of the relativistic case
Gauge and supergauge field theories
International Nuclear Information System (INIS)
The most actual problems concerning gauge fields are reviwed. Theoretical investigations conducted since as early as 1954 are enclosed. Present status of gauge theories is summarized, including intermediate vector mesons, heavy leptons, weak interactions of hadrons, V-A structure, universal interaction, infrared divergences in perturbation theory, particle-like solutions in gauge theories, spontaneous symmetry breaking. Special emphasis is placed on strong interactions, or more precisely, on the alleged unobservability of ''color'' objects (quark confinement). Problems dealing with the supersymmetric theories invariant under gauge transformations and spontaneous breaking of supersymmetry are also discussed. Gauge theories are concluded to provide self-consistent apparatus for weak and electromagnetic interactions. As to strong interactions such models are still to be discovered
Confinement and duality in supersymmetric gauge theories
Giacomelli, Simone
2013-01-01
In this thesis we review the Seiberg-Witten solution of four dimensional N=2 gauge theories, the six-dimensional construction of these models recently proposed by Gaiotto and the BPS quiver technique for the determination of the BPS spectrum of N=2 theories. We then study how these recent developments allow to better understand nonperturbative aspects such as confinement and dynamical symmetry breaking in the N=1 theories obtained starting from N=2 SQCD and adding a mass term for the chiral multiplet in the adjoint of the gauge group. We find an unusual realization of the 't Hooft-Mandelstam mechanism, in which confinement and dynamical symmetry breaking are due to the condensation of different degrees of freedom.
Chiral perturbation theory with nucleons
International Nuclear Information System (INIS)
I review the constraints posed on the interactions of pions, nucleons and photons by the spontaneously broken chiral symmetry of QCD. The framework to perform these calculations, chiral perturbation theory, is briefly discussed in the meson sector. The method is a simultaneous expansion of the Greens functions in powers of external moments and quark masses around the massless case, the chiral limit. To perform this expansion, use is made of a phenomenological Lagrangian which encodes the Ward-identities and pertinent symmetries of QCD. The concept of chiral power counting is introduced. The main part of the lectures of consists in describing how to include baryons (nucleons) and how the chiral structure is modified by the fact that the nucleon mass in the chiral limit does not vanish. Particular emphasis is put on working out applications to show the strengths and limitations of the methods. Some processes which are discussed are threshold photopion production, low-energy compton scattering off nucleons, πN scattering and the σ-term. The implications of the broken chiral symmetry on the nuclear forces are briefly described. An alternative approach, in which the baryons are treated as very heavy fields, is touched upon
Introduction to gauge theories
International Nuclear Information System (INIS)
These lecture notes contain the text of five lectures and a Supplement. The lectures were given at the JINR-CERN School of Physics, Tabor, Czechoslovakia, 5-18 June 1983. The subgect of the lecinvariancetures: gauge of electromagnetic and weak interactions, higgs and supersymmetric particles. The Supplement contains reprints (or excerpts) of some classical papers on gauge invariance by V. Fock, F. London, O. Klein and H. Weyl, in which the concept of gauge invariance was introduced and developed
Geometrical formalism in gauge theories
Kubyshin, Yuri A.
2003-01-01
We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the quantization of gauge theories. Some results for bundles over two-dimensional spaces are presented.
Hard amplitudes in gauge theories
International Nuclear Information System (INIS)
In this lecture series 1 presents recent developments in perturbation theory methods for gauge theories for processes with many partons. These techniques and results are useful in the calculation of cross sections for processes with many final state partons which have applications in the study of multi-jet phenomena in high-energy colliders. The results illuminate many important and interesting properties of non-abelian gauge theories. 30 refs., 9 figs
Notoph gauge theory: superfield formalism
International Nuclear Information System (INIS)
We derive absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the 4D free Abelian 2-form gauge theory by exploiting the superfield approach to BRST formalism. The antisymmetric tensor gauge field of the above theory was christened as the 'notoph' (i.e., the opposite of 'photon') gauge field by Ogievetsky and Polubarinov way back in 1966-67. We briefly outline the problems involved in obtaining the absolute anticommutativity of the (anti-)BRST formalism. One of the highlights of our results is the emergence of a Curci-Ferrari type of restriction in the context of 4D Abelian 2-form (notoph) gauge theory which renders the nilpotent (anti-)BRST symmetries of the theory to be absolutely anticommutative in nature
International Nuclear Information System (INIS)
Pure Yang-Mills theory is reformulated in terms of gauge-independent loop variables whose intrinsic redundancy is removed using a newly derived nonabelian generalisation of the Poincare lemma. (author)
Gauge theory webs and surfaces
Erdoğan, Ozan; Sterman, George
2011-01-01
We analyze the perturbative cusp and closed polygons of Wilson lines for massless gauge theories in coordinate space, and express them as exponentials of two-dimensional integrals. These integrals have geometric interpretations, which link renormalization scales with invariant distances.
Gauge mediation in string theory
Kawano, Teruhiko; Ooguri, Hirosi; Ookouchi, Yutaka
2007-01-01
We show that a large class of phenomenologically viable models for gauge mediation of supersymmetry breaking based on meta-stable vacua can be realized in local Calabi–Yau compactifications of string theory.
Gauge Theories of Vector Particles
Glashow, S. L.; Gell-Mann, M.
1961-04-24
The possibility of generalizing the Yang-Mills trick is examined. Thus we seek theories of vector bosons invariant under continuous groups of coordinate-dependent linear transformations. All such theories may be expressed as superpositions of certain "simple" theories; we show that each "simple theory is associated with a simple Lie algebra. We may introduce mass terms for the vector bosons at the price of destroying the gauge-invariance for coordinate-dependent gauge functions. The theories corresponding to three particular simple Lie algebras - those which admit precisely two commuting quantum numbers - are examined in some detail as examples. One of them might play a role in the physics of the strong interactions if there is an underlying super-symmetry, transcending charge independence, that is badly broken. The intermediate vector boson theory of weak interactions is discussed also. The so-called "schizon" model cannot be made to conform to the requirements of partial gauge-invariance.
Collisions in Chiral Kinetic Theory.
Chen, Jing-Yuan; Son, Dam T; Stephanov, Mikhail A
2015-07-10
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order O(ℏ), which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the H function obeying Boltzmann's H theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing the chiral vortical effect. PMID:26207458
Collisions in Chiral Kinetic Theory
Chen, Jing-Yuan; Stephanov, Mikhail A
2015-01-01
Using a covariant formalism, we construct a chiral kinetic theory Lorentz invariant to order $\\mathcal O(\\hbar)$ which includes collisions. We find a new contribution to the particle number current due to the side jumps required by the conservation of angular momentum during collisions. We also find a conserved symmetric stress-energy tensor as well as the $H$-function obeying Boltzmann's $H$-theorem. We demonstrate their use by finding a general equilibrium solution and the values of the anomalous transport coefficients characterizing chiral vortical effect.
Staggered chiral random matrix theory
International Nuclear Information System (INIS)
We present a random matrix theory for the staggered lattice QCD Dirac operator. The staggered random matrix theory is equivalent to the zero-momentum limit of the staggered chiral Lagrangian and includes all taste breaking terms at their leading order. This is an extension of previous work which only included some of the taste breaking terms. We will also present some results for the taste breaking contributions to the partition function and the Dirac eigenvalues.
Gauge theory loop operators and Liouville theory
International Nuclear Information System (INIS)
We propose a correspondence between loop operators in a family of four dimensional N=2 gauge theories on S4 - including Wilson, 't Hooft and dyonic operators - and Liouville theory loop operators on a Riemann surface. This extends the beautiful relation between the partition function of these N=2 gauge theories and Liouville correlators found by Alday, Gaiotto and Tachikawa. We show that the computation of these Liouville correlators with the insertion of a Liouville loop operator reproduces Pestun's formula capturing the expectation value of a Wilson loop operator in the corresponding gauge theory. We prove that our definition of Liouville loop operators is invariant under modular transformations, which given our correspondence, implies the conjectured action of S-duality on the gauge theory loop operators. Our computations in Liouville theory make an explicit prediction for the exact expectation value of 't Hooft and dyonic loop operators in these N=2 gauge theories. The Liouville loop operators are also found to admit a simple geometric interpretation within quantum Teichmueller theory as the quantum operators representing the length of geodesics. We study the algebra of Liouville loop operators and show that it gives evidence for our proposal as well as providing definite predictions for the operator product expansion of loop operators in gauge theory. (orig.)
Topological Summation in Lattice Gauge Theory
Bietenholz, Wolfgang
2012-01-01
In gauge theories the field configurations often occur in distinct topological sectors. In a lattice regularised system with chiral fermions, these sectors can be defined by referring to the Atiyah-Singer Index Theorem. However, if such a model is simulated with local updates of the lattice gauge configuration, the Monte Carlo history tends to get stuck in one sector for many steps, in particular on fine lattices. Then expectation values can be measured only within specific sectors. Here we present a pilot study in the 2-flavour Schwinger model which explores methods of approximating the complete result for an observable - corresponding to a suitable sum over all sectors - based on numerical measurements in a few specific topological sectors. We also probe various procedures for an indirect evaluation of the topological susceptibility, starting from such topologically restricted measurements.
Quantum principal bundles and corresponding gauge theories
Durdevic, M
1995-01-01
A generalization of classical gauge theory is presented, in the framework of a noncommutative-geometric formalism of quantum principal bundles over smooth manifolds. Quantum counterparts of classical gauge bundles, and classical gauge transformations, are introduced and investigated. A natural differential calculus on quantum gauge bundles is constructed and analyzed. Kinematical and dynamical properties of corresponding gauge theories are discussed.
Functional determinants in gauge theory and string theory
International Nuclear Information System (INIS)
Determinants arise whenever Gaussian functional integrals are evaluated. As a result, they are pervasive in physics. In this thesis the author studied, in a mathematically precise fashion, some questions concerning functional determinants in Quantum Field Theory and String Theory. The emphasis is on deriving explicit general identities which can be applied to physical problems. In Chapters 1-3, he studies determinants of families of Weyl operators on compact manifolds. The motivation for this work comes from Chiral Gauge Theory. In a theory containing chiral Fermions coupled to Bosons y, a partial integration in the functional integral over the Fermi fields yields terms involving determinants of Weyl operators ∂y. In Chapter 4 he turns his attention to a problem in String Theory. In the Polyakov formulation of string perturbation theory, the partition function and scattering amplitudes are calculated as sums of contributions from different world sheet topologies. The contribution from surfaces of a particular topology is given by a functional integral, which, after gauge-fixing, can be expressed as an integral of a certain measure over an appropriate moduli space. For an arbitrary finite group acting on a compact manifold, he defines an analytic torsion for the invariant subcomplex of the de Rham complex, generalizing the definition given by Ray and Singer in the absence of a group action. Motivated by the work of Quillen, he uses this torsion to define a natural norm on the determinant line of the invariant cohomology
Gell-Mann-Oaks-Renner-like relation in infrared-conformal gauge theories
International Nuclear Information System (INIS)
A generalization of the Gell-Mann-Oaks-Renner relation to the case of infrared-conformal gauge theories is discussed. The starting point is the chiral Ward identity connecting the isovector pseudoscalar susceptibility to the chiral condensate, in a mass-deformed theory. A renormalization-group analysis shows that the pseudoscalar susceptibility is not saturated by the lightest state, but a contribution from the continuum part of the spectrum survives in the chiral limit. The computation also shows how infrared-conformal gauge theories behave differently, depending on whether the anomalous dimension of the chiral condensate be smaller or larger than 1. An application to lattice simulations is briefly discussed.
Machines for lattice gauge theory
Energy Technology Data Exchange (ETDEWEB)
Mackenzie, P.B.
1989-05-01
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig.
Machines for lattice gauge theory
International Nuclear Information System (INIS)
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig
Confinement and lattice gauge theory
International Nuclear Information System (INIS)
The motivation for formulating gauge theories on a lattice to study non-perturbative phenomena is reviewed, and recent progress supporting the compatibility of asymptotic freedom and quark confinement in the standard SU(3) Yang-Mills theory of the strong interaction is discussed
Gravity: a gauge theory perspective
Nester, James M
2016-01-01
The evolution of a generally covariant theory is under-determined. One hundred years ago such dynamics had never before been considered; its ramifications were perplexing, its future important role for all the fundamental interactions under the name gauge principle could not be foreseen. We recount some history regarding Einstein, Hilbert, Klein and Noether and the novel features of gravitational energy that led to Noether's two theorems. Under-determined evolution is best revealed in the Hamiltonian formulation. We developed a covariant Hamiltonian formulation. The Hamiltonian boundary term gives covariant expressions for the quasi-local energy, momentum and angular momentum. Gravity can be considered as a gauge theory of the local Poincar\\'e group. The dynamical potentials of the Poincar\\'e gauge theory of gravity are the frame and the connection. The spacetime geometry has in general both curvature and torsion. Torsion naturally couples to spin; it could have a significant magnitude and yet not be noticed,...
Gauge Theories, Tessellations & Riemann Surfaces
He, Yang-Hui
2014-01-01
We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories. These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere. On higher genus they give rise to intricate patterns. Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WUNing; ZHANGDa-Hua; RUANTu-Nan
2003-01-01
DitTerential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence between quantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gauge theory of gravity is studied.
Recent developments in lattice gauge theories
International Nuclear Information System (INIS)
Since 1980 most of the work on QCD has involved Monte Carlo simulations of lattice gauge theories. In this report I will review these works, emphasizing the most recent and/or the most accurate ones. This talk will be divided into three parts. i) Results from theories with no dynamical quarks. These include a determination of the string tension and the spectra of quarkless mesons (glueballs). ii) Inclusion of quarks in the quenched approximation. The topics discussed include chiral symmetry breaking, hadronic spectra and static properties of hadrons. iii) Caveats. Some of the studies on the validity of the quenched approximation and the problems brought on by the practical restrictions on lattice sizes are presented. This discussion will be restricted to color SU(3) and zero temperature
Chiral phase transition in a lattice fermion-gauge-scalar model with U(1) gauge symmetry
International Nuclear Information System (INIS)
The chiral phase transition induced by a charged scalar field is investigated numerically in a lattice fermion-gauge-scalar model with U(1) gauge symmetry, proposed recently as a model for dynamical fermion mass generation. For very strong gauge coupling the transition is of second order and its scaling properties are very similar to those of the Nambu-Jona-Lasinio model. However, in the vicinity of the tricritical point at somewhat weaker coupling, where the transition changes the order, the scaling behavior is different. Therefore it is worthwhile to investigate the continuum limit of the model at this point. (orig.)
Quenched Chiral Perturbation Theory to one loop
Colangelo, G.; Pallante, E.
1998-01-01
The divergences of the generating functional of quenched Chiral Perturbation theory (qCHPT) to one loop are computed in closed form. We show how the quenched chiral logarithms can be reabsorbed in the renormalization of the B0 parameter of the leading order Lagrangian. Finally, we do the chiral powe
Strong Coupling Gauge Theories in LHC ERA
Fukaya, H.; Harada, M.; Tanabashi, M.; Yamawaki, K.
2011-01-01
AdS/QCD, light-front holography, and the nonperturbative running coupling / Stanley J. Brodsky, Guy de Teramond and Alexandre Deur -- New results on non-abelian vortices - Further insights into monopole, vortex and confinement / K. Konishi -- Study on exotic hadrons at B-factories / Toru Iijima -- Cold compressed baryonic matter with hidden local symmetry and holography / Mannque Rho -- Aspects of baryons in holographic QCD / T. Sakai -- Nuclear force from string theory / K. Hashimoto -- Integrating out holographic QCD back to hidden local symmetry / Masayasu Harada, Shinya Matsuzaki and Koichi Yamawaki -- Holographic heavy quarks and the giant Polyakov loop / Gianluca Grignani, Joanna Karczmarek and Gordon W. Semenoff -- Effect of vector-axial-vector mixing to dilepton spectrum in hot and/or dense matter / Masayasu Harada and Chihiro Sasaki -- Infrared behavior of ghost and gluon propagators compatible with color confinement in Yang-Mills theory with the Gribov horizon / Kei-Ichi Kondo -- Chiral symmetry breaking on the lattice / Hidenori Fukaya [for JLQCD and TWQCD collaborations] -- Gauge-Higgs unification: Stable Higgs bosons as cold dark matter / Yutaka Hosotani -- The limits of custodial symmetry / R. Sekhar Chivukula ... [et al.] -- Higgs searches at the tevatron / Kazuhiro Yamamoto [for the CDF and D[symbol] collaborations] -- The top triangle moose / R. S. Chivukula ... [et al.] -- Conformal phase transition in QCD like theories and beyond / V. A. Miransky -- Gauge-Higgs unification at LHC / Nobuhito Maru and Nobuchika Okada -- W[symbol]W[symbol] scattering in Higgsless models: Identifying better effective theories / Alexander S. Belyaev ... [et al.] -- Holographic estimate of Muon g - 2 / Deog Ki Hong -- Gauge-Higgs dark matter / T. Yamashita -- Topological and curvature effects in a multi-fermion interaction model / T. Inagaki and M. Hayashi -- A model of soft mass generation / J. Hosek -- TeV physics and conformality / Thomas Appelquist -- Conformal
Gyrocenter-gauge kinetic theory
Energy Technology Data Exchange (ETDEWEB)
H. Qin; W. M. Tang; W. W. Lee
2000-08-07
Gyrocenter-gauge kinetic theory is developed as an extension of the existing gyrokinetic theories. In essence, the formalism introduced here is a kinetic description of magnetized plasmas in the gyrocenter coordinates which is fully equivalent to the Vlasov-Maxwell system in the particle coordinates. In particular, provided the gyroradius is smaller than the scale-length of the magnetic field, it can treat high frequency range as well as the usual low frequency range normally associated with gyrokinetic approaches. A significant advantage of this formalism is that it enables the direct particle-in-cell simulations of compressional Alfven waves for MHD applications and of RF waves relevant to plasma heating in space and laboratory plasmas. The gyrocenter-gauge kinetic susceptibility for arbitrary wavelength and arbitrary frequency electromagnetic perturbations in a homogeneous magnetized plasma is shown to recover exactly the classical result obtained by integrating the Vlasov-Maxwell system in the particle coordinates. This demonstrates that all the waves supported by the Vlasov-Maxwell system can be studied using the gyrocenter-gauge kinetic model in the gyrocenter coordinates. This theoretical approach is so named to distinguish it from the existing gyrokinetic theory, which has been successfully developed and applied to many important low-frequency and long parallel wavelength problems, where the conventional meaning of gyrokinetic has been standardized. Besides the usual gyrokinetic distribution function, the gyrocenter-gauge kinetic theory emphasizes as well the gyrocenter-gauge distribution function, which sometimes contains all the physics of the problems being studied, and whose importance has not been realized previously. The gyrocenter-gauge distribution function enters Maxwell's equations through the pull-back transformation of the gyrocenter transformation, which depends on the perturbed fields. The efficacy of the gyrocenter-gauge kinetic approach
Two-color gauge theory with novel infrared behavior.
Appelquist, T; Brower, R C; Buchoff, M I; Cheng, M; Fleming, G T; Kiskis, J; Lin, M F; Neil, E T; Osborn, J C; Rebbi, C; Schaich, D; Schroeder, C; Syritsyn, S; Voronov, G; Vranas, P; Witzel, O
2014-03-21
Using lattice simulations, we study the infrared behavior of a particularly interesting SU(2) gauge theory, with six massless Dirac fermions in the fundamental representation. We compute the running gauge coupling derived nonperturbatively from the Schrödinger functional of the theory, finding no evidence for an infrared fixed point up through gauge couplings g(2) of order 20. This implies that the theory either is governed in the infrared by a fixed point of considerable strength, unseen so far in nonsupersymmetric gauge theories, or breaks its global chiral symmetries producing a large number of composite Nambu-Goldstone bosons relative to the number of underlying degrees of freedom. Thus either of these phases exhibits novel behavior. PMID:24702347
Towards Deriving Higgs Lagrangian from Gauge Theories
Kitazawa, N; Kitazawa, Noriaki; Sannino, Francesco
1998-01-01
A new method of deriving the Higgs Lagrangian from vector-like gauge theories is explored. After performing a supersymmetric extension of gauge theories we identify the auxiliary field associated with the "meson" superfield, in the low energy effective theory, as the composite Higgs field. The auxiliary field, at tree level, has a "negative squared mass". By computing the one-loop effective action in the low energy effective theory, we show that a kinetic term for the auxiliary field emerges when an explicit non-perturbative mechanism for supersymmetry breaking is introduced. We find that, due to the naive choice of the Kaehler potential, the Higgs potential remains unbounded from the below. A possible scenario for solving this problem is presented. It is also shown that once chiral symmetry is spontaneously broken via a non-zero vacuum expectation value of the Higgs field, the low energy composite fermion field acquires a mass and decouples, while in the supersymmetric limit it was kept massless by the 't Ho...
Entwinement in discretely gauged theories
Balasubramanian, V; Craps, B; De Jonckheere, T; Galli, F
2016-01-01
We develop the notion of entwinement to characterize the amount of quantum entanglement between internal, discretely gauged degrees of freedom in a quantum field theory. This concept originated in the program of reconstructing spacetime from entanglement in holographic duality. We define entwinement formally in terms of a novel replica method which uses twist operators charged in a representation of the discrete gauge group. In terms of these twist operators we define a non-local, gauge-invariant object whose expectation value computes entwinement in a standard replica limit. We apply our method to the computation of entwinement in symmetric orbifold conformal field theories in 1+1 dimensions, which have an $S_N$ gauging. Such a theory appears in the weak coupling limit of the D1-D5 string theory which is dual to AdS$_3$ at strong coupling. In this context, we show how certain kinds of entwinement measure the lengths, in units of the AdS scale, of non-minimal geodesics present in certain excited states of the...
Differential renormalization of gauge theories
Energy Technology Data Exchange (ETDEWEB)
Aguila, F. del; Perez-Victoria, M. [Dept. de Fisica Teorica y del Cosmos, Universidad de Granada, Granada (Spain)
1998-10-01
The scope of constrained differential renormalization is to provide renormalized expressions for Feynman graphs, preserving at the same time the Ward identities of the theory. It has been shown recently that this can be done consistently at least to one loop for Abelian and non-Abelian gauge theories. We briefly review these results, evaluate as an example the gluon self energy in both coordinate and momentum space, and comment on anomalies. (author) 9 refs, 1 fig., 1 tab
International Nuclear Information System (INIS)
We exhibit the role of Hochschild cohomology in quantum field theory with particular emphasis on gauge theory and Dyson-Schwinger equations, the quantum equations of motion. These equations emerge from Hopf- and Lie algebra theory and free quantum field theory only. In the course of our analysis, we exhibit an intimate relation between the Slavnov-Taylor identities for the couplings and the existence of Hopf sub-algebras defined on the sum of all graphs at a given loop order, surpassing the need to work on single diagrams
String Theory and Gauge Theories (Strings, Gravity, and the Large N Limit of Gauge Theories)
International Nuclear Information System (INIS)
We will see how gauge theories, in the limit that the number of colors is large, give string theories. We will discuss some examples of particular gauge theories where the corresponding string theory is known precisely, starting with the case of the maximally supersymmetric theory in four dimensions which corresponds to ten dimensional string theory. We will discuss recent developments in this area.
Gauge theory and variational principles
Bleecker, David
2005-01-01
This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field
Gauge theory of collective modes
International Nuclear Information System (INIS)
The classical theory of Riemann ellipsoids is formulated naturally as a gauge theory based on a principal G-bundle P. The structure group G = SO(3) is the vorticity group and the bundle P = GL+ (3, ℝ) is the connected component of the general linear group. The base manifold is the space of positive-definite real 3 × 3 symmetric matrices, identified geometrically with the space of inertia ellipsoids. Non-holonomic constraints determine connections on the bundle. In particular, the trivial connection corresponds to rigid body motion, the natural Riemannian connection to irrotational flow and the invariant connection to the falling cat. The curvature form determines the fluid's field tensor which is an analogue of the familiar Faraday tensor. Associated G-bundles and the covariant derivative yield new quantum geometrical collective models that are a natural generalization of the Bohr model. These new geometric structures formulate the collective model as a Yang-Mills gauge theory.
Quantization of Galilean gauge theories
International Nuclear Information System (INIS)
Galilean gauge theories are quantized according to Dirac's theory of canonical quantization of constrained systems. Only the zero-momentum term in the Fourier expansion of the gauge fields is compatible with the constraints, and it is different from zero for periodic boundary conditions, while it is zero if the fields are required to vanish on the surface of the quantization box. Such a term has physical effects which therefore depend on boundary conditions. The effect of the zero-momentum term of the electric potential is to forbid charged states. This constraint holds both in the Abelian and non-Abelian case and it is true also in the relativistic theory. The zero-momentum term of the magnetic potential in the Abelian case gives rise to only radiative corrections (which are the c→infinity limit of the relativistic ones), while in the non-Abelian case it also affects the matter-field interaction
Gauge fields without perturbation theory
International Nuclear Information System (INIS)
Methods for investigating gauge theories not based on perturbation theory have been considered. It is pointed out that the Monte-Carlo method is the most powerful one for gauge lattice theories. This method is indicative of the absence of phase transition in SU(3)-gluodynamics. Spectrum of lower hadrons as well as a number of other physical values disregarding quark polarization of vacuum, are calculated by this method. The method of expansion in the inverse number of the degrees of feedom proved to be very interesting and promiing for understanding qualitative picture of calculations in QCD. The study of gluodynamics in D-meric space-time is reduced to the study of O-meric tasks, which constituted the main achievement in the study of multicolour QCD for the last year
Studies of gauge field theories in terms of local gauge-invariant quantities
International Nuclear Information System (INIS)
In the framework of the functional-integral approach to quantum gauge field theories in the present thesis a quantization procedure in terms of gauge-invariant fields is proposed and realized on the example of two- and four-dimensional Abelian models (Thirring model and QED) as well as the one-flavour QCD. For this the algebra of from the gauge-dependent field configuration of the basing quantum field theory formed gauge-invariant Grassmann-algebra valued differential forms, which carries the structure of a Z2-graded differential algebra, is studied in more detail. Thereafter follows the implementation of a suitable chosen set of gauge-invariant fields as well as certain algebraic relations into the functional integral, by which the original gauge-dependent field configuration can be integrated out. This procedure called ''reduction of the functional integral'' leads finally to an effective bosonized (quantum) theory of interacting gauge-invariant and by this physical fields. The presented procedure can be considered as general bosonization scheme for quantum field theories in arbitrary space-time dimensions. The physical evaluation of the obtained effective theories is demonstrated on the example of the calculation of the chiral anomaly as well as certain vacuum expectation values in the framework of the studied Abelian models. As it is thereby shown one is confronted with a series of novel phenomena and problems, which allow at suitable treatment deeper insights in non-perturbative questions
Phase transitions for SU(N) gauge theories with arbitrary number of flavors
Jora, Renata
2015-01-01
We study the phase diagram of an $SU(N)$ gauge theory in terms of the number of colors $N$ and flavors $N_f$ with emphasis on the confinement and chiral symmetry breaking phases. We argue that as opposed to SUSY QCD there is a small region in the $(N,N_f)$ plane where the theory has the chiral symmetry broken but it is unconfined. The possibility of a new phase with strong confinement and chiral symmetry breaking is suggested.
Minimal anomaly-free chiral fermion sets and gauge coupling unification
Cebola, Luis M; Felipe, R Gonzalez; Simoes, C
2014-01-01
We look for minimal chiral sets of fermions beyond the Standard Model that are anomaly-free and, simultaneously, vector-like particles with respect to colour SU(3) and electromagnetic U(1). We then study whether the addition of such particles to the Standard Model particle content allows for the unification of gauge couplings at a high energy scale, above $5.0 \\times 10^{15}$ GeV so as to be safely consistent with proton decay bounds. The possibility to have unification at the string scale is also considered. Inspired in grand unified theories, we also search for minimal chiral fermion sets that belong to SU(5) multiplets. Restricting to representations up to dimension 50, we show that some of these sets can lead to gauge unification at the GUT and/or string scales.
International Nuclear Information System (INIS)
We present gauge theories of gravitation based, respectively, on the general linear group GL(n, R) and its inhomogeneous extension IGL(n, R). [SO(n-1,1) and ISO(n-1,1) for torsion-free manifolds]. Noting that the geometry of the conventional gauge theories can be described in terms of a principal fiber bundle, and that their action is a scalar in such a superspace, we construct principal fiber bundles based on the above gauge groups and propose to describe gravitation in terms of their corresponding scalar curvatures. To ensure that these manifolds do indeed have close ties with the space-time of general relativity, we make use of the notion of the parallel transport of vector fields in space-time to uniquely relate the connections in space-time to the gauge potentials in fiber bundles. The relations turn out to be similar to that suggested earlier by Yang. The actions we obtain are related to those of Einstein and Yang but are distinct from both and have an Einstein limit. The inclusion of internal symmetry leads to the analogs of Einstein-Yang-Mills equations. A number of variations and less attractive alternatives based on the subgroups of the above groups are also discussed
Random Matrix Theory and Chiral Logarithms
Berbenni-Bitsch, M. E.; Göckeler, M.; Hehl, H.; Meyer, S.; Rakow, P. E. L.; Schäfer, A.; Wettig, T.
1999-01-01
Abstract: Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).
Asymptotically Free Gauge Theories. I
Wilczek, Frank; Gross, David J.
1973-07-01
Asymptotically free gauge theories of the strong interactions are constructed and analyzed. The reasons for doing this are recounted, including a review of renormalization group techniques and their application to scaling phenomena. The renormalization group equations are derived for Yang-Mills theories. The parameters that enter into the equations are calculated to lowest order and it is shown that these theories are asymptotically free. More specifically the effective coupling constant, which determines the ultraviolet behavior of the theory, vanishes for large space-like momenta. Fermions are incorporated and the construction of realistic models is discussed. We propose that the strong interactions be mediated by a "color" gauge group which commutes with SU(3)xSU(3). The problem of symmetry breaking is discussed. It appears likely that this would have a dynamical origin. It is suggested that the gauge symmetry might not be broken, and that the severe infrared singularities prevent the occurrence of non-color singlet physical states. The deep inelastic structure functions, as well as the electron position total annihilation cross section are analyzed. Scaling obtains up to calculable logarithmic corrections, and the naive lightcone or parton model results follow. The problems of incorporating scalar mesons and breaking the symmetry by the Higgs mechanism are explained in detail.
Scattering amplitudes in gauge theories
Henn, Johannes M
2014-01-01
At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum ...
Weak interactions and gauge theories
International Nuclear Information System (INIS)
The status of the electroweak gauge theory, also known as quantum asthenodynamics (QAD), is examined. The major result is that the standard WS-GIM model describes the data well, although one should still look for signs of further complexity and better tests of its gauge theory aspect. A second important result is that the measured values of the three basic coupling constants of present-energy physics, g/sub s/, g, and √(5/3)g' of SU(3)/sub c/ x SU(2)2 x U(1), are compatible with the idea that these interactions are unified at high energies. Much of the paper deals with open questions, and it takes up the following topics: the status of QAD, the scalar meson spectrum, the fermion spectrum, CP violation, and decay dynamics. 118 references, 20 figures
Sigma-model representation of gauge theories
International Nuclear Information System (INIS)
A new formulation of gauge theories in terms of the eight-dimensional nonlinear sigma-model is presented. The basic quantity is the principal chiral field b(x,y) with values in the relevant group algebra, xsub(μ) being identified as the usual Minkowski 4-coordinate. The Yang-Mills field is defined as bsub(μ)(x). The higher components in the y-expansion of b(x,y) are shown to be removable at the expense of bsub(μ)(x) by imposing on b(x,Y) certain covariant constraints. This procedure results in the ''string'' representation for b(x,y) in terms of the path-ordered integral of bsub(μ)(x) along a fixed path between points (x+y),x. The standard source-free Yang-Mills equations are found to be equivalent to the continuity equation (with respect to y-differentiation) for the Cartan form associated with some particular b(x, y). The striking analogy with ordinary sigma-models suggests that the symmetric, gauge-invariant phase of the Yang-Mills theory may be described most adequately within the corresponding eight-dimensional linear sigma-model
Cohomological analysis of gauged-fixed gauge theories
Barnich, G; Hurth, Tobias; Skenderis, K; Barnich, Glenn; Henneaux, Marc; Hurth, Tobias; Skenderis, Kostas
2000-01-01
The relation between the gauge-invariant local BRST cohomology involving the antifields and the gauge-fixed BRST cohomology is clarified. It is shown in particular that the cocycle conditions become equivalent once it is imposed, on the gauge-fixed side, that the BRST cocycles should yield deformations that preserve the nilpotency of the (gauge-fixed) BRST differential. This shows that the restrictions imposed on local counterterms by the Quantum Noether condition in the Epstein--Glaser construction of gauge theories are equivalent to the restrictions imposed by BRST invariance on local counterterms in the standard Lagrangian approach.
On integration over Fermi fields in chiral and supersymmetric theories
International Nuclear Information System (INIS)
Chiral and supersymmetric theories are considered which cannot be formulated directly in Euclidean space or regularized by means of massive fields in a manifestly gauge invariant fashion. In case of so called real representations a simple recipe is proposed which allows for unambiguous evaluation of the fermionic determinant circumventing the difficulties mentioned. As application of the general technique the effective fermionic interactions induced by instantons of small size within simplest chiral and supesymmetric theories are calculated (SU(2) as the gauge group and one doublet of Weyl spinors or a triplet of Majorana spinors, respectively). In the latter case the effective Lagrangian violates explicitly invariance under supersymmetric transformations on the fermionic and vector fields defined in standard way
Renormalizable Quantum Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning
2002-01-01
The quantum gravity is formulated based on the principle of local gauge invariance. The model discussedin this paper has local gravitational gauge symmetry, and gravitational field is represented by gauge field. In the leading-order approximation, it gives out classical Newton's theory of gravity. In the first-order approximation and for vacuum,it gives out Einstein's general theory of relativity. This quantum gauge theory of gravity is a renormalizable quantumtheory.
Theorems for Asymptotic Safety of Gauge Theories
Bond, Andrew D
2016-01-01
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasized. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated.
Scattering amplitudes in gauge theories
International Nuclear Information System (INIS)
First monographical text on this fundamental topic. Course-tested, pedagogical and self-contained exposition. Includes exercises and solutions. At the fundamental level, the interactions of elementary particles are described by quantum gauge field theory. The quantitative implications of these interactions are captured by scattering amplitudes, traditionally computed using Feynman diagrams. In the past decade tremendous progress has been made in our understanding of and computational abilities with regard to scattering amplitudes in gauge theories, going beyond the traditional textbook approach. These advances build upon on-shell methods that focus on the analytic structure of the amplitudes, as well as on their recently discovered hidden symmetries. In fact, when expressed in suitable variables the amplitudes are much simpler than anticipated and hidden patterns emerge. These modern methods are of increasing importance in phenomenological applications arising from the need for high-precision predictions for the experiments carried out at the Large Hadron Collider, as well as in foundational mathematical physics studies on the S-matrix in quantum field theory. Bridging the gap between introductory courses on quantum field theory and state-of-the-art research, these concise yet self-contained and course-tested lecture notes are well-suited for a one-semester graduate level course or as a self-study guide for anyone interested in fundamental aspects of quantum field theory and its applications. The numerous exercises and solutions included will help readers to embrace and apply the material presented in the main text.
Introduction to lattice gauge theory
International Nuclear Information System (INIS)
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs
Is the chiral U(1) theory trivial?
International Nuclear Information System (INIS)
The chiral U(1) theory differs from the corresponding vector theory by an imaginary contribution to the effective action which amounts to a phase factor in the partition function. The vector theory, i.e. QED, is known to be trivial in the continuum limit. It is argued that the presence of the phase factor will not alter this result and the chiral theory is non-interacting as well. (orig.)
Chiral kinetic theory and anomalous hydrodynamics in even spacetime dimensions
Dwivedi, Vatsal
2016-01-01
We study the hydrodynamics of a gas of noninteracting Weyl fermions coupled to the electromagnetic field in $(2N + 1) + 1$ spacetime dimensions using the chiral kinetic theory, which encodes the gauge anomaly in the Chern character of the nonabelian Berry connection over the Fermi surface. We derive the anomalous contributions to the relativistic hydrodynamic currents in equilibrium and at a finite temperature, which agree with and provides an approach complementary to the results derived previously using thermodynamic constraints.
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.)
Invariance, symmetry and periodicity in gauge theories
International Nuclear Information System (INIS)
The interplay between gauge transformations and coordinate transformations is discussed; the theory will aid in understanding the mixing of space-time and internal degrees of freedom. The subject is presented under the following headings: coordinate transformation laws for arbitrary fields, coordinate transformation laws for gauge fields, properties of symmetric gauge fields, construction of symmetric gauge fields, physical significance of gauge transformations, and magnetic monopole topology without Higgs fields. The paper ends with conclusions and suggestions for further research
Introduction to gauge theories of electroweak interactions
International Nuclear Information System (INIS)
These lectures are meant to serve a twofold purpose. First, they contain an introduction to electroweak gauge theories for those who are not (or not yet) specialized in particle theory. The author tries to emphasize the physical requirements which almost inevitably lead to the concept of gauge theories. The second aim is to provide a background for the more advanced courses, in particular on grand unified theories and on dynamical symmetry breaking. Therefore, the emphasis is mostly on the properties of a general gauge theory and the standard model is then discussed as the simplest example to illustrate those properties. The author is concerned only with the perturbative aspects of gauge theories. (Auth.)
Geometric Formulation of Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
WU Ning; ZHANG Da-Hua; RUAN Tu-Nan
2003-01-01
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantumgauge theory of gravity is formulated completely in the framework of traditional quantum field theory. In order to studythe relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curvedspace, it is important to set up the geometry picture of quantum gauge theory of gravity. The correspondence betweenquantum gauge theory of gravity and differential geometry is discussed and the geometry picture of quantum gaugetheory of gravity is studied.
Anomalies of the Entanglement Entropy in Chiral Theories
Iqbal, Nabil
2015-01-01
We study entanglement entropy in theories with gravitational or mixed U(1) gauge-gravitational anomalies in two, four and six dimensions. In such theories there is an anomaly in the entanglement entropy: it depends on the choice of reference frame in which the theory is regulated. We discuss subtleties regarding regulators and entanglement entropies in anomalous theories. We then study the entanglement entropy of free chiral fermions and self-dual bosons and show that in sufficiently symmetric situations this entanglement anomaly comes from an imbalance in the flux of modes flowing through the boundary, controlled by familiar index theorems. In two and four dimensions we use anomalous Ward identities to find general expressions for the transformation of the entanglement entropy under a diffeomorphism. (In the case of a mixed anomaly there is an alternative presentation of the theory in which the entanglement entropy is not invariant under a U(1) gauge transformation. The free-field manifestation of this pheno...
Neutrino mass in gauge theories
International Nuclear Information System (INIS)
The question of neutrino mass is discussed in the context of gauge theories. The astrophysical and cosmological motivations are presented, along with the constraints that they impose on the properties of neutrinos. This is followed by a discussion on various SU(2)/sub L/ x U(1)/sub Y/ models which incorporate massive neutrinos. Some aspects of the phenomenology are also discussed, with special emphasis on the radiative decay of massive neutrinos. In all but one SU(2)/sub L/ x U(1)/sub Y/ model, the lifetime is so large that the photon flux from the decay of background relic neutrinos is too small to observe if the neutrino mass is in the range of a few tens of eVs. To gain more insight about neutrino masses, larger gauge groups are considered. SU(2)/sub L/ x SU(2)/sub R/ x U(1)/sub B-L/ models can give rise to an interesting hierarchy of masses of light neutrinos. In a minimal model, such a hierarchy is inconsistent with cosmological constraints. In grand unified theories such as SD(10), the neutrino mass matrix is related to the masses of other elementary fermions
Gauge Invariants and Correlators in Flavoured Quiver Gauge Theories
Mattioli, Paolo
2016-01-01
In this paper we study the construction of holomorphic gauge invariant operators for general quiver gauge theories with flavour symmetries. Using a characterisation of the gauge invariants in terms of equivalence classes generated by permutation actions, along with representation theory results in symmetric groups and unitary groups, we give a diagonal basis for the 2-point functions of holomorphic and anti-holomorphic operators. This involves a generalisation of the previously constructed Quiver Restricted Schur operators to the flavoured case. The 3-point functions are derived and shown to be given in terms of networks of symmetric group branching coefficients. The networks are constructed through cutting and gluing operations on the quivers.
Symmetry breaking thermal fluctuations in gauge theories
International Nuclear Information System (INIS)
Boundary conditions in field theories usually play the role of an infrared cutoff. The authors show that the situation is more subtle in gauge theories. Since the gauge field is a string rather than a point variable, boundary conditions may create qualitatively new gauge invariant degrees of freedom. This kinematical construction and its dynamics are discussed in the case of SU(2) and SU(3) theories with periodic boundary conditions
On the infrared stability of gauge theories
International Nuclear Information System (INIS)
We consider a class of field theories which contains a Lorentz and gauge invariant theory as a fixed point, but whose generic member possesses none of these symmetries. We show that this fixed point is an infrared repulsor for all non-abelian groups. We also discuss the case of the N=4 supersymmetric gauge theory whose stability properties are shown to depend on the gauge group
Unphysical phases in staggered chiral perturbation theory
Aubin, Christopher; Colletti, Katrina; Davila, George
2016-04-01
We study the phase diagram for staggered quarks using chiral perturbation theory. In beyond-the-standard-model simulations using a large number (>8 ) of staggered fermions, unphysical phases appear for coarse enough lattice spacing. We argue that chiral perturbation theory can be used to interpret one of these phases. In addition, we show that only three broken phases for staggered quarks exist, at least for lattice spacings in the regime a2≪ΛQCD2 .
Gauge theories and magnetic charge
International Nuclear Information System (INIS)
If the magnetic field for an exact gauge group H (assumed compact and connected) exhibits an inverse square law behaviour at large distances then the generalized magnetic charge, appearing as the coefficient, completely determines the topological quantum number of the solution. When this magnetic charge operator is expressed as a linear combination of mutually commuting generators of H, the components are uniquely determined, up to the action of the Weyl group, and have to be weights of a new group Hsup(γ) which is explicitly constructed out of H. The relation between the 'electric' group H and the 'magnetic' group Hsup(γ) is symmetrical in the sense that (Hsup(γ))sup(γ)=H. The results suggest that H monopoles are Hsup(γ) multiplets and vice versa and that the true symmetry group is HxHsup(γ). In this duality topological and Noether quantum numbers exchange roles rather as in Sine-Gordon theory. A physical possibility is that H and Hsup(γ) be the colour and weak electromagnetic gauge groups. (Auth.)
Staggered Heavy Baryon Chiral Perturbation Theory
Bailey, Jon A
2007-01-01
Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms the order of the cubed pion mass, which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms the order of the squared lattice spacing. The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in d...
Coulomb branches for rank 2 gauge groups in 3d N=4 gauge theories
Hanany, Amihay
2016-01-01
The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare and dressed BPS monopole operators. We utilise the conformal dimension to define a fan which, upon intersection with the weight lattice of a GNO-dual group, gives rise to a collection of semi-groups. It turns out that the unique Hilbert bases of these semi-groups are a sufficient, finite set of monopole operators which generate the entire chiral ring. Moreover, the knowledge of the properties of the minimal generators is enough to compute the Hilbert series explicitly. The techniques of this paper allow an efficient evaluation of the Hilbert series for general rank gauge groups. As an application, we provide various examples for all rank two gauge groups to demonstrate the novel interpretation.
Cascading gauge theory on dS4 and String Theory landscape
International Nuclear Information System (INIS)
Placing anti-D3 branes at the tip of the conifold in Klebanov–Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e., there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes
Phase diagram of a lattice U(1) gauge theory with gauge fixing
International Nuclear Information System (INIS)
As a first step towards a nonperturbative investigation of the gauge-fixing (Rome) approach to lattice chiral gauge theories we study a U(1) model with an action that includes a local gauge-fixing term and a mass counterterm for the gauge fields. The model is studied on the trivial orbit so that only the dynamics of the longitudinal gauge degrees of freedom is taken into account. Mean-field and numerical calculations reveal that the phase diagram of this open-quotes reducedclose quotes model contains, in addition to ferromagnetic (FM), antiferromagnetic (AM) and paramagnetic (PM) phases, also a novel so-called helicoidal ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing condensate of the vector field. The continuum limit is defined by approaching the FM-FMD phase transition from within the FM phase. We show that the global U(1) symmetry is restored in this continuum limit, both numerically and in perturbation theory. The numerical results for the magnetization in the FM and FMD phases are in good agreement with perturbation theory. copyright 1998 The American Physical Society
On the Phase Diagram of a Lattice U(1) Gauge Theory with Gauge Fixing
Bock, W; Shamir, Y; Bock, Wolfgang; Golterman, Maarten; Shamir, Yigal
1998-01-01
As a first step towards a nonperturbative investigation of the gauge-fixing (Rome) approach to lattice chiral gauge theories we study a U(1) model with an action that includes a local gauge-fixing term and a mass counterterm for the gauge fields. The model is studied on the trivial orbit so that only the dynamics of the longitudinal gauge degrees of freedom is taken into account. The phase diagram of this higher-derivative scalar field theory is determined, both in the mean-field approximation and numerically. The continuum limit of the model corresponds to a continuous phase transition between a ferromagnetic (FM) phase where the global U(1) symmetry is broken, and a so-called helicoidal ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing condensate of the vector field. The global U(1) symmetry is restored in this continuum limit. We show that our data for the magnetization in the FM and FMD phases are in good agreement with perturbation theory.
Lattice Gauge Theories and Spin Models
Mathur, Manu
2016-01-01
The Wegner $Z_2$ gauge theory-$Z_2$ Ising spin model duality in $(2+1)$ dimensions is revisited and derived through a series of canonical transformations. These $Z_2$ results are directly generalized to SU(N) lattice gauge theory in $(2+1)$ dimensions to obtain a dual SU(N) spin model in terms of the SU(N) magnetic fields and electric scalar potentials. The gauge-spin duality naturally leads to a new gauge invariant disorder operator for SU(N) lattice gauge theory. A variational ground state of the dual SU(2) spin model with only nearest neighbour interactions is constructed to analyze SU(2) lattice gauge theory.
Introduction to gauge theories and unification
International Nuclear Information System (INIS)
This paper contains the following lectures on gauge theories: basic notations; dimensional regularization; complex scalar field theory; scalar field theory; self-interacting scalar field theory; Noether's theorem; spontaneous symmetry breaking; dirac field theories; local symmetry; quantum electrodynamics; Higgs mechanism; non-Abelian symmetries; and Weinberg-Salam-Glashow theory
Exact formulas in noncommutative gauge theories
Wallet, Jean-Christophe
2016-01-01
The noncommutative space $\\mathbb{R}^3_\\lambda$, a deformation of $\\mathbb{R}^3$, supports a $3$-parameter family of gauge theory models with gauge-invariant harmonic term, stable vacuum and which are perturbatively finite to all orders. Properties of this family are discussed. The partition function factorizes as an infinite product of reduced partition functions, each one corresponding to the reduced gauge theory on one of the fuzzy spheres entering the decomposition of $\\mathbb{R}^3_\\lambda$. For a particular sub-family of gauge theories, each reduced partition function is exactly expressible as a ratio of determinants. A relation with integrable 2-D Toda lattice hierarchy is indicated.
Gravity, Gauge Theories and Geometric Algebra
Lasenby, Anthony; Doran, Chris; Gull, Stephen
2004-01-01
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical ...
Homotopical Poisson reduction of gauge theories
Paugam, Frederic
2011-01-01
The classical Poisson reduction of a given Lagrangian system with (local) gauge symmetries has to be done before its quantization. We propose here a coordinate free and self-contained mathematical presentation of the covariant Batalin-Vilkovisky Poisson reduction of a general gauge theory. It was explained in physical terms (DeWitt indices) in Henneaux and Teitelboim's book on quantization of gauge theories. It was studied in coordinates using jet spaces by Barnich-Brandt-Henneaux and Stashef...
Staggered heavy baryon chiral perturbation theory
Bailey, Jon A.
2008-03-01
Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms of O(mπ3), which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms of O(a2). The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.
Loop formulation of gauge theory and gravity
Loll, R.
1993-01-01
This chapter contains a overview of the loop formulation of Yang-Mills theory and 3+1-dimensional gravity in the Ashtekar form. Since the configuration space of these theories are spaces of gauges potentials, their classical and quantum descriptions may be given in terms of gauges-invariant Wilson
New identities among gauge theory amplitudes
Bjerrum-Bohr, N. E. J.; Damgaard, Poul H.; Feng, Bo; Søndergaard, Thomas
2010-08-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N = 4 super Yang-Mills multiplet.
New identities among gauge theory amplitudes
Energy Technology Data Exchange (ETDEWEB)
Bjerrum-Bohr, N.E.J., E-mail: bjbohr@nbi.d [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Feng Bo [Center of Mathematical Science, Zhejiang University, Hangzhou (China); Kavli Institute for Theoretical Physics China, CAS, Beijing 100190 (China); Sondergaard, Thomas [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen (Denmark)
2010-08-09
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
New Identities among Gauge Theory Amplitudes
Bjerrum-Bohr, N E J; Feng, Bo; Sondergaard, Thomas
2010-01-01
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
General Relativity as a constrained Gauge Theory
Cianci, R.; Vignolo, S.; Bruno, D
2006-01-01
The formulation of General Relativity presented in math-ph/0506077 and the Hamiltonian formulation of Gauge theories described in math-ph/0507001 are made to interact. The resulting scheme allows to see General Relativity as a constrained Gauge theory.
New identities among gauge theory amplitudes
International Nuclear Information System (INIS)
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
Toward a gauge field theory of gravity.
Yilmaz, H.
Joint use of two differential identities (Bianchi and Freud) permits a gauge field theory of gravity in which the gravitational energy is localizable. The theory is compatible with quantum mechanics and is experimentally viable.
Gravitation as Gauge theory of Poincare Group
International Nuclear Information System (INIS)
The geometrical approach to gauge theories, based on fiber-bundles, is shown in detail. Several gauge formalisms for gravitation are examined. In particular, it is shown how to build gauge theories for non-semisimple groups. A gravitational theory for the Poincare group, with all the essential characteristics of a Yang-Mills theory is proposed. Inonu-Wigner contractions of gauge theories are introduced, which provide a Lagrangian formalism, equivalent to a Lagrangian de Sitter theory supplemented by weak constraints. Yang and Einstein theories for gravitation become particular cases of a Yang-Mills theory. The classical limit of the proposed formalism leads to the Poisson equation, for the static case. (Author)
Spectroscopy of gauge theories based on exceptional Lie groups
International Nuclear Information System (INIS)
We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E6 and E7, up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and revisit the self-dual exceptional models. We study the chiral ring of G2 to degree 13, as well as a few classical groups. The homological dimension of a ring is a natural estimator of its complexity and provides a guideline for identifying theories that have a good chance to be amenable to a solution. (author)
Tests of Chiral Perturbation Theory with COMPASS
Friedrich, Jan
2010-01-01
The COMPASS experiment at the CERN SPS studies with high precision pion-photon induced reactions via the Primakoff effect on nuclear targets. This offers the test of chiral perturbation theory (ChPT) in various channels: Pion Compton scattering allows to clarify the long-standing question of the pion polarisabilities, single neutral pion production is related to the chiral anomaly, and for the two-pion production cross sections exist as yet untested ChPT predictions.
Tests of Chiral Perturbation Theory with COMPASS
International Nuclear Information System (INIS)
The COMPASS experiment at CERN studies with high precision pion-photon induced reactions on nuclear targets via the Primakoff effect. This offers the possibility to test chiral perturbation theory (ChPT) in various channels: Pion Compton scattering allows to clarify the longstanding question of the pion polarisabilities, single neutral pion production is related to the chiral anomaly, and for the two-pion production cross sections exist as yet untested ChPT predictions.
SUSY gauge theory on graded manifolds
Sardanashvily, G.; Wachowski, W.
2014-01-01
Lagrangian classical field theory of even and odd fields is adequately formulated in terms of fibre bundles and graded manifolds. In particular, conventional Yang-Mills gauge theory is theory of connections on smooth principal bundles, but its BRST extension involves odd ghost fields an antifields on graded manifolds. Here, we formulate Yang-Mills theory of Grassmann-graded gauge fields associated to Lie superalgebras on principal graded bundles. A problem lies in a geometric definition of od...
Diagrammatics of braided group gauge theory
Majid, S
1996-01-01
We develop a gauge theory or theory of bundles and connections on them at the level of braids and tangles. Extending recent algebraic work, we provide now a fully diagrammatic treatment of principal bundles, a theory of global gauge transformations, associated braided fiber bundles and covariant derivatives on them. We describe the local structure for a concrete Z_3-graded or `anyonic' realization of the theory.
Semidirect gauge mediation in conformal windows of vectorlike gauge theories
International Nuclear Information System (INIS)
Direct gauge mediation models using the Intriligator-Seiberg-Shih metastable vacua suffer from the Landau pole problem of the standard-model gauge couplings and the existence of R-symmetry forbidding gaugino masses. These problems may be solved by using the recently proposed supersymmetry (SUSY)-breaking models in a conformal window of the vectorlike SU(NC) gauge theory with gauge singlets. In this paper we propose a model of gauge mediation based on the SUSY-breaking model in the conformal window, and study the dynamics for SUSY breaking. In this model, there are massive vectorlike bifundamental fields charged under both SU(NC) and the standard-model gauge group, and our model can be regarded as a semidirect gauge mediation model. The color number NC can be small to avoid the Landau pole problem, and R symmetry is also broken under a reasonable assumption on the strong dynamics of the model. The model possesses only one free parameter, and the gaugino and sfermion masses are naturally of the same order.
On Yang--Mills Theories with Chiral Matter at Strong Coupling
Energy Technology Data Exchange (ETDEWEB)
Shifman, M.; /Minnesota U., Theor. Phys. Inst. /Saclay, SPhT; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept.
2008-08-20
Strong coupling dynamics of Yang-Mills theories with chiral fermion content remained largely elusive despite much effort over the years. In this work, we propose a dynamical framework in which we can address non-perturbative properties of chiral, non-supersymmetric gauge theories, in particular, chiral quiver theories on S{sub 1} x R{sub 3}. Double-trace deformations are used to stabilize the center-symmetric vacuum. This allows one to smoothly connect smaller(S{sub 1}) to larger(S{sub 1}) physics (R{sub 4} is the limiting case) where the double-trace deformations are switched off. In particular, occurrence of the mass gap in the gauge sector and linear confinement due to bions are analytically demonstrated. We find the pattern of the chiral symmetry realization which depends on the structure of the ring operators, a novel class of topological excitations. The deformed chiral theory, unlike the undeformed one, satisfies volume independence down to arbitrarily small volumes (a working Eguchi-Kawai reduction) in the large N limit. This equivalence, may open new perspectives on strong coupling chiral gauge theories on R{sub 4}.
Gauge theories in anti-selfdual variables
Bochicchio, M.; Pilloni, A.
2013-01-01
Some years ago the Nicolai map, viewed as a change of variables from the gauge connection in a fixed gauge to the anti-selfdual part of the curvature, has been extended by the first named author to pure YM from its original definition in N=1 SUSY YM. We study here the perturbative 1PI effective action in the anti-selfdual variables of any gauge theory, in particular pure YM, QCD and N=1 SUSY YM. We prove that the one-loop 1PI effective action of a gauge theory mapped to the anti-selfdual vari...
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
Dimer models and quiver gauge theories
Pichai, Ramadevi
2013-12-01
= 1 quiver gauge theories on coincident D3 branes placed at a tip of a Calabi-Yau singularity C are dual to string theories on AdS5×X5 where X5 are Sasaki-Einstein spaces. We present a neat combinatorial approach called dimer model to understand interrelations between toric quiver gauge theories and toric data representing the Calabi-Yau singularities.
Prepotential Formulation of Lattice Gauge Theory
Raychowdhury, Indrakshi; Anishetty, Ramesh
2014-01-01
Within the Hamiltonian formulation of Lattice gauge theories, prepotentials, belonging to the fundamental representation of the gauge group and defined locally at each site of the lattice, enables us to construct local loop operators and loop states. We propose a set of diagrammatic rules for the action of local gauge invariant operators on arbitrary loop states. Moreover We propose a new set of fusion variables within the prepotential aproach suitable for approaching the weak coupling limit.
Gauge theory of gravity and matter
Kerr, Steven
2014-01-01
It is shown how to write the first order action for gravity in a gauge theoretic formalism where the spin connection and frame field degrees of freedom are assimilated together into a gauge connection. It is then shown how to couple the theory to spin-0, 1/2, 1 and 3/2 fields in a gauge invariant fashion. The results hold in any number of spacetime dimensions.
Lorentz Gauge Theory and Spinor Interaction
Carlevaro, Nakia; Montani, Giovanni
2008-01-01
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.
Lorentz Gauge Theory and Spinor Interaction
Carlevaro, Nakia; Lecian, Orchidea Maria; Montani, Giovanni
A gauge theory of the Lorentz group, based on the different behavior of spinors and vectors under local transformations, is formulated in a flat space-time and the role of the torsion field within the generalization to curved space-time is briefly discussed. The spinor interaction with the new gauge field is then analyzed assuming the time gauge and stationary solutions, in the non-relativistic limit, are treated to generalize the Pauli equation.
Comment on the Adler-Bardeen theorem in non-Abelian gauge theories
International Nuclear Information System (INIS)
It is pointed out that the constructive proof of the Adler-Bardeen theorem for the chiral and scale (counting identity) anomalies in non-Abelian gauge theories proceeds just as in the spinor electrodynamics, although several interesting features characteristic of non-Abelian theories appear. (author)
Quaternion gauge theory of dyonic fields
International Nuclear Information System (INIS)
Outlining the idea of quaternion non-Abelian gauge formalism and that of the structural symmetry between generalized fields of dyons and gravito-dyons, it is shown that this formulation characterizes the Abelian and non-Abelian structure of dyons in terms of pure real and imaginary unit quaternions. Extending this formalism to the case of gravito-dyons it has been shown that pure imaginary unit quaternions advocate the curvature in the theory of gravito-dyons and hence the SL(2,c) gauge group of gravitation plays the same role as that of SU(2) gauge group does in non-Abelian gauge theory. Furthermore, we have unified the theories of electromagnetism and gravitation in terms of single parameter α by means of quaternion-gauge formalism and the corresponding field equations have also been derived in a unique and consistent way. (author)
Quaternion gauge theory of dyonic fields
Energy Technology Data Exchange (ETDEWEB)
Bisht, P.S. (Kumaun Univ., Almora (India). Dept. of Physics); Negi, O.P.S.; Rajput, B.S.
1991-01-01
Outlining the idea of quaternion non-Abelian gauge formalism and that of the structural symmetry between generalized fields of dyons and gravito-dyons, it is shown that this formulation characterizes the Abelian and non-Abelian structure of dyons in terms of pure real and imaginary unit quaternions. Extending this formalism to the case of gravito-dyons it has been shown that pure imaginary unit quaternions advocate the curvature in the theory of gravito-dyons and hence the SL(2,c) gauge group of gravitation plays the same role as that of SU(2) gauge group does in non-Abelian gauge theory. Furthermore, we have unified the theories of electromagnetism and gravitation in terms of single parameter {alpha} by means of quaternion-gauge formalism and the corresponding field equations have also been derived in a unique and consistent way. (author).
Lattice methods in gauge theories beyond the standard model
International Nuclear Information System (INIS)
We report extended simulation results and their new analysis in two important gauge theories with twelve fermion flavors in the fundamental SU(3) color representation and two fermions in the sextet representation. We probe the Nf=12 model with respect to the conformal window using mass deformed finite size scaling (FSS) theory driven by the fermion mass anomalous dimension. Our results at fixed gauge coupling show problems with the conformal scenario of the Nf=12 model. In the sextet model with two flavors, under the conformal hypothesis, we determine large values for the anomalous fermion mass dimension with γ ≥ 1. Since our sextet analysis favors the chiral symmetry breaking hypothesis without conformality, the large exponent γ could play an important role in understanding the composite Higgs mechanism. The new results discussed here include our extended data sets and exceed what was presented at the conference. (author)
Pion momentum distributions in the nucleon in chiral effective theory
Burkardt, M; Ji, Chueng-Ryong; Melnitchouk, W; Thomas, A W
2012-01-01
We compute the light-cone momentum distributions of pions in the nucleon in chiral effective theory using both pseudovector and pseudoscalar pion-nucleon couplings. For the pseudovector coupling we identify \\delta-function contributions associated with end-point singularities arising from the pion-nucleon rainbow diagrams, as well as from pion tadpole diagrams which are not present in the pseudoscalar model. Gauge invariance is demonstrated, to all orders in the pion mass, with the inclusion of Weinberg-Tomozawa couplings involving operator insertions at the \\pi NN vertex. The results pave the way for phenomenological applications of pion cloud models that are manifestly consistent with the chiral symmetry properties of QCD.
Riemannian gauge theory and charge quantization
International Nuclear Information System (INIS)
In a traditional gauge theory, the matter fields φa and the gauge fields Aμc are fundamental objects of the theory. The traditional gauge field is similar to the connection coefficient in the riemannian geometry covariant derivative, and the field-strength tensor is similar to the curvature tensor. In contrast, the connection in riemannian geometry is derived from the metric or an embedding space. Guided by the physical principal of increasing symmetry among the four forces, we propose a different construction. Instead of defining the transformation properties of a fundamental gauge field, we derive the gauge theory from an embedding of a gauge fiber F = Rn or F = Cn into a trivial, embedding vector bundle F-tilde = RN or F-tilde = CN where N > n. Our new action is symmetric between the gauge theory and the riemannian geometry. By expressing gauge-covariant fields in terms of the orthonormal gauge basis vectors, we recover a traditional, SO(n) or U(n) gauge theory. In contrast, the new theory has all matter fields on a particular fiber couple with the same coupling constant. Even the matter fields on a C1 fiber, which have a U(1) symmetry group, couple with the same charge of ±q. The physical origin of this unique coupling constant is a generalization of the general relativity equivalence principle. Because our action is independent of the choice of basis, its natural invariance group is GL(n,R) or GL(n,C). Last, the new action also requires a small correction to the general-relativity action proportional to the square of the curvature tensor. (author)
Numerical techniques for lattice gauge theories
International Nuclear Information System (INIS)
The motivation for formulating gauge theories on a lattice is reviewed. Monte Carlo simulation techniques are then discussed for these systems. Finally, the Monte Carlo methods are combined with renormalization group analysis to give strong numerical evidence for confinement of quarks by non-Abelian gauge fields
Conformal Fixed Points of Unidentified Gauge Theories
Polyakov, A M
2004-01-01
In this article we discuss gauge/strings correspondence based on the non-critical strings. With this goal we present several remarkable sigma models with the AdS target spaces. The models have kappa symmetry and are completely integrable. The radius of the AdS space is fixed and thus they describe isolated fixed points of gauge theories in various dimensions
Principles of gauge theory of real hadrons
International Nuclear Information System (INIS)
Complete analysis of Lagrangian structure of hadron three-particle interaction, invariant as to gauge transformations, generated by vector representation of the Lorentz complete group, was carried out. Qualitative evaluations of several problems of particle physics in the framework of the Lorentz-vector gauge theory of hadrons are provided. 1 ref
Is SU(3) Chiral Perturbation Theory an Effective Field Theory?
Holstein, Barry R.
1998-01-01
We argue that the difficulties associated with the convergence properties of conventional SU(3) chiral perturbation theory can be ameliorated by use of a cutoff, which suppresses the model-dependent short distance effects in such calculations.
Reducible gauge theories in very special relativity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker, E-mail: sudhakerupadhyay@gmail.com [Department of Physics, Indian Institute of Technology Kanpur, 208016, Kanpur (India)
2015-12-14
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb–Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb–Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin–Vilkovisy (BV) formulation in VSR.
Reducible gauge theories in very special relativity
Energy Technology Data Exchange (ETDEWEB)
Upadhyay, Sudhaker [Indian Institute of Technology Kanpur, Department of Physics, Kanpur (India)
2015-12-15
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb-Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb-Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin-Vilkovisy (BV) formulation in VSR. (orig.)
Reducible gauge theories in very special relativity
International Nuclear Information System (INIS)
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb-Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb-Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin-Vilkovisy (BV) formulation in VSR. (orig.)
Reducible gauge theories in very special relativity
International Nuclear Information System (INIS)
In this paper we analyze the tensor field (reducible gauge) theories in the context of very special relativity (VSR). Particularly, we study the VSR gauge symmetry as well as VSR BRST symmetry of Kalb–Ramond and Abelian 3-form fields involving a fixed null vector. We observe that the Kalb–Ramond and Abelian 3-form fields and corresponding ghosts get masses in the VSR framework. The effective action in VSR-type axial gauge is greatly simplified compared with the VSR-type Lorenz gauge. Further, we quantize these models using a Batalin–Vilkovisy (BV) formulation in VSR
Topologically Massive Gauge Theory: A Lorentzian Solution
Saygili, K.
2006-01-01
We obtain a lorentzian solution for the topologically massive non-abelian gauge theory on AdS space by means of a SU(1, 1) gauge transformation of the previously found abelian solution. There exists a natural scale of length which is determined by the inverse topological mass. The topological mass is proportional to the square of the gauge coupling constant. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (an...
Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
Chung, Hee-Joong
2016-01-01
We calculate partition function and correlation functions in A-twisted 2d $\\mathcal{N}=(2,2)$ theories and topologically twisted 3d $\\mathcal{N}=2$ theories containing adjoint chiral multiplet with particular choices of $R$-charges and the magnetic fluxes for flavor symmetries. According to Gauge-Bethe correspondence, they correspond to Heisenberg XXX and XXZ spin chain models. We identify the partition function as the inverse of the norm of the Bethe eigenstates. Correlation functions are identified as the coefficients of the expectation value of Baxter $Q$-operators. In addition, we consider correlation functions of 2d $\\mathcal{N}=(2,2)^*$ theory and their relation to equivariant quantum cohomology and equivariant integration of cotangent bundle of Grassmann manifolds. Also, we study the ring relations of supersymmetric Wilson loops in 3d $\\mathcal{N}=2^*$ theory and Bethe subalgebra of XXZ spin chain model.
Features of a Simple IR Conformal Gauge Theory
Landa-Marban, David; Hip, Ivan
2013-01-01
The Schwinger model with $N_{f} \\geq 2$ flavors is a simple example for an IR conformal gauge theory. We consider numerical data for two light flavors, based on simulations with dynamical chiral lattice fermions. We test properties and predictions that were put forward for IR conformal models in the recent literature. In particular we probe the decorrelation of low lying Dirac eigenvalues, and we discuss the mass anomalous dimension and its IR extrapolation. Here we encounter subtleties, which may urge caution with analogous efforts in other models, such as multi-flavor QCD.
Yang-Mills theory in Coulomb gauge
International Nuclear Information System (INIS)
In this thesis we study the Yang-Mills vacuum structure by using the functional Schroedinger picture in Coulomb gauge. In particular we discuss the scenario of colour confinement, which was originally formulated by Gribov. After a short introduction, we recall some basic aspects of Yang-Mills theories, its canonical quantization in the Weyl gauge and the functional Schroedinger picture. We then consider the minimal Coulomb gauge and the Gribov problem of the gauge theory. The gauge fixing of the Coulomb gauge is done by using the Faddeev-Popov method, which enables the resolution of the Gauss law - the constraint on physical states. In the third chapter, we variationally solve the stationary Yang-Mills Schroedinger equation in Coulomb gauge for the vacuum state. Therefor we use a vacuum wave functional, which is strongly peaked at the Gribov horizon. The vacuum energy functional is calculated and minimized resulting in a set of coupled Schwinger-Dyson equations for the gluon energy, the ghost and Coulomb form factors and the curvature in gauge orbit space. Using the angular approximation these integral equations have been solved analytically in both the infrared and the ultraviolet regime. The asymptotic analytic solutions in the infrared and ultraviolet regime are reasonably well reproduced by the full numerical solutions of the coupled Schwinger-Dyson equations. In the fourth chapter, we investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. (orig.)
Quantum Simulation of Non-Abelian Lattice Gauge Theories
Bögli, Michael
2013-01-01
We use quantum link models to construct a quantum simulator for U(N) and SU(N) lattice gauge theories. These models replace Wilson's classical link variables by quantum link operators, reducing the link Hilbert space to a finite number of dimensions. We show how to embody these quantum link models with fermionic matter with ultracold alkaline-earth atoms using optical lattices. Unlike classical simulations, a quantum simulator does not suffer from sign problems and can thus address the corresponding dynamics in real time. Using exact diagonalization results we show that these systems share qualitative features with QCD, including chiral symmetry breaking and we study the expansion of a chirally restored region in space in real time.
Higher Spin Gauge Theories in Various Dimensions
Vasilev, M A
2004-01-01
Properties of nonlinear higher spin gauge theories of totally symmetric massless higher spin fields in anti-de Sitter space of any dimension are discussed with the emphasize on the general aspects of the approach.
Introduction to dualities in gauge theories
International Nuclear Information System (INIS)
These notes present a pedagogical introduction to magnetic monopoles, supersymmetry and dualities in gauge theories. They are based on lectures given at the X Jorge Andre Swieca Summer School on Particles and Fields. (author)
Introduction to gauge theories of electroweak interactions
International Nuclear Information System (INIS)
Intended as a lecture for physicists who are not familiar with the sophisticated theoretical models in particle physics. Starting with the standard gauge model of electromagnetic, weak and strong interactions the recent developments of a unified gauge theory of electroweak interactions are shown. Shortcomings in the unitarity problem of the V-A fermi theory of charged intermediate vector bosons. Presented are the spontaneous symmetry breaking in quantum mechanics, the abelian higgs model as an example of a spontaneously broken gauge field theory, the minimal gauge group of electroweak interactions, the fermion mass generation. Further on the anomalies in quantum field theory are discussed and the radiative corrections to the vector boson masses are considered. (H.B.)
Gauge Theories on the Light-Front
Brodsky, S J
2004-01-01
The light-front quantization of gauge theories in light-cone gauge provides a frame-independent wavefunction representation of relativistic bound states, simple forms for current matrix elements, explicit unitary, and a trivial vacuum. The light-front Hamiltonian form of QCD provides an alternative to lattice gauge theory for the computation of nonperturbative quantities such as the hadronic spectrum and the corresponding eigenfunctions. In the case of the electroweak theory, spontaneous symmetry breaking is represented by the appearance of zero modes of the Higgs field. Light-front quantization then leads to an elegant ghost-free theory of massive gauge particles, automatically incorporating the Lorentz and 't Hooft conditions, as well as the Goldstone boson equivalence theorem.
Gauge/String Duality in Confining Theories
Edelstein, J D; Edelstein, Jose D.; Portugues, Ruben
2006-01-01
This is the content of a set of lectures given at the XIII Jorge Andre Swieca Summer School on Particles and Fields, held in Campos do Jordao, Brazil in January 2005. They intend to be a basic introduction to the topic of gauge/gravity duality in confining theories. We start by reviewing some key aspects of the low energy physics of non-Abelian gauge theories. Then, we present the basics of the AdS/CFT correspondence and its extension both to gauge theories in different spacetime dimensions with sixteen supercharges and to more realistic situations with less supersymmetry. We discuss the different options of interest: placing D-branes at singularities and wrapping D-branes in calibrated cycles of special holonomy manifolds. We finally present an outline of a number of non-perturbative phenomena in non-Abelian gauge theories as seen from supergravity.
Development of unified gauge theories: retrospect
International Nuclear Information System (INIS)
The construction and development of unified gauge theory of weak, electromagnetic, and strong interactions is reviewed. The Weinberg and Lee contributions to this study are mainly considered as personal recollections
Gauge coupling renormalization in orbifold field theories
Choi, Kiwoon; Kim, Hyung Do; Kim, Ian-Woo
2002-01-01
We investigate the gauge coupling renormalization in orbifold field theories preserving 4-dimensional N=1 supersymmetry in the framework of 4-dimensional effective supergravity. As a concrete example, we consider the 5-dimensional Super-Yang-Mills theory on a slice of AdS_5. In our approach, one-loop gauge couplings can be determined by the loop-induced axion couplings and the tree level properties of 4-dimensional effective supergravity which are much easier to be computed.
Chiral effective field theory and nuclear forces
Machleidt, R
2011-01-01
We review how nuclear forces emerge from low-energy QCD via chiral effective field theory. The presentation is accessible to the non-specialist. At the same time, we also provide considerable detailed information (mostly in appendices) for the benefit of researchers who wish to start working in this field.
Gauge Theory of Gravity and Spacetime
Hehl, Friedrich W
2012-01-01
The advent of general relativity settled it once and for all that a theory of spacetime is inextricably linked to the theory of gravity. From the point of view of the gauge principle of Weyl and Yang-Mills-Utiyama, it became manifest around the 1960s (Sciama--Kibble) that gravity is closely related to the Poincare group acting in Minkowski space. The gauging of this external group induces a Riemann-Cartan geometry on spacetime. If one generalizes the gauge group of gravity, one finds still more involved spacetime geometries. If one specializes it to the translation group, one finds a specific Riemann-Cartan geometry with teleparallelism (Weitzenbock geometry).
A Microscopic Theory of Gauge Mediation
International Nuclear Information System (INIS)
We construct models of indirect gauge mediation where the dynamics responsible for breaking supersymmetry simultaneously generates a weakly coupled subsector of messengers. This provides a microscopic realization of messenger gauge mediation where the messenger and hidden sector fields are unified into a single sector. The UV theory is SQCD with massless and massive quarks plus singlets, and at low energies it flows to a weakly coupled quiver gauge theory. One node provides the primary source of supersymmetry breaking, which is then transmitted to the node giving rise to the messenger fields. These models break R-symmetry spontaneously, produce realistic gaugino and sfermion masses, and give a heavy gravitino.
Microscopic quantum superpotential in Script N = 1 gauge theories
Ferrari, Frank
2007-10-01
We consider the Script N = 1 super Yang-Mills theory with gauge group U(N), adjoint chiral multiplet X and tree-level superpotential Tr W(X). We compute the quantum effective superpotential Wmic as a function of arbitrary off-shell boundary conditions at infinity for the scalar field X. This effective superpotential has a remarkable property: its critical points are in one-to-one correspondence with the full set of quantum vacua of the theory, providing in particular a unified picture of solutions with different ranks for the low energy gauge group. In this sense, Wmic is a good microscopic effective quantum superpotential for the theory. This property is not shared by other quantum effective superpotentials commonly used in the literature, like in the strong coupling approach or the glueball superpotentials. The result of this paper is a first step in extending Nekrasov's microscopic derivation of the Seiberg-Witten solution of Script N = 2 super Yang-Mills theories to the realm of Script N = 1 gauge theories.
Relating lattice QCD and chiral perturbation theory
International Nuclear Information System (INIS)
We present simulation results for lattice QCD using chiral lattice fermions, which obey the Ginsparg Wilson relation. After discuss first conceptual issues, and then numerical results. In the epsilon regime we evaluated the low lying modes in Dirac spectrum and the axial correlation functions for very light quarks. These provide information about the leading low energy constants in chiral perturbation theory: the pion decay constant and the scalar condensate. In the p regime we measured light meson masses, the PCAC quark mass and the renormalisation constant ZA
Random Lattice QCD and chiral effective theories
Pavlovsky, O. V.
2004-01-01
Resent developments in the Random Matrix and Random Lattice Theories give a possibility to find low-energy theorems for many physical models in the Born-Infeld form. In our approach that based on the Random Lattice regularization of QCD we try to used the similar ideas in the low-energy baryon physics for finding of the low-energy theory for the chiral fields in the strong-coupling regime.
On the entanglement entropy for gauge theories
Ghosh, Sudip; Soni, Ronak; Trivedi, Sandip
2015-01-01
We propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and Non-Abelian gauge theories. For ℤ N $$ {\\mathbb{Z}}_N $$ and U(1) theories, without matter, our definition agrees with a particular case of the definition given by Casini, Huerta and Rosabal. We also argue that in general, both for Abelian and Non-Abelian theories, our definition agrees with the entanglemen...
Torsion as a Gauge Field in a Lorentz-Chern-Simons Theory
del Pino, Simón
2016-01-01
We explore a model of gravity that arises from the consideration of the Chern-Simons form in 2+1 dimensions for a spin connection with a contorsion described by a scalar and a vector field. The effective Lagrangian presents a local Weyl symmetry allowing us to gauge the scalar field to a constant value. From a gauge field theory perspective, it is shown that the vector part of the torsion (related to its trace) is a gauge field for the Weyl group, which allows the interpretation of the torsion as an electromagnetic field. In the gauge of constant scalar field we obtain Chiral Gravity coupled to a Chern-Simons-Proca theory for the vector field, that at the level of equations of motion is equivalent to Topologically Massive Electrodynamics minimally coupled to Chiral Gravity. Electrodynamics and gravity appear here unified as geometrical features of a Riemann-Cartan manifold.
Perturbative Quantum Gravity from Gauge Theory
Bern, Zvi; Johansson, Henrik
2010-01-01
In a previous paper we observed that (classical) tree-level gauge theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we suggest that this duality persists to all quantum loop orders and can thus be used to obtain multi-loop gravity amplitudes easily from gauge-theory ones. As a non-trivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a non-supersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an anti-symmetric tensor and dilaton.
The chiral anomaly from M theory
Gursoy, U; Portugues, R; Gursoy, Umut; Hartnoll, Sean A.; Portugues, Ruben
2003-01-01
We argue that the chiral anomaly of $\\Ncal = 1$ super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous $U(1)_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of ``massive isometry'' to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric.
A primer for Chiral Perturbative Theory
International Nuclear Information System (INIS)
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
A primer for Chiral Perturbative Theory
Energy Technology Data Exchange (ETDEWEB)
Scherer, Stefan [Mainz Univ. (Germany). Inst. fuer Kernphysik; Schindler, Matthias R. [South Carolina Univ., Columbia, SC (United States). Dept. of Physics; George Washington Univ., Washington, DC (United States). Dept. of Physics
2012-07-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques. (orig.)
A primer for chiral perturbation theory
Scherer, Stefan
2012-01-01
Chiral Perturbation Theory, as effective field theory, is a commonly accepted and well established working tool, approximating quantum chromodynamics at energies well below typical hadron masses. This volume, based on a number of lectures and supplemented with additional material, provides a pedagogical introduction for graduate students and newcomers entering the field from related areas of nuclear and particle physics. Starting with the the Lagrangian of the strong interactions and general symmetry principles, the basic concepts of Chiral Perturbation Theory in the mesonic and baryonic sectors are developed. The application of these concepts is then illustrated with a number of examples. A large number of exercises (81, with complete solutions) are included to familiarize the reader with helpful calculational techniques.
A gauge-invariant reorganization of thermal gauge theory
International Nuclear Information System (INIS)
This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in mD/T, mf/T and e2, where mD and mf are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e ∝ 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in mD/T and g2, where mD is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T ∝ 2 - 3 Tc. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)
A gauge-invariant reorganization of thermal gauge theory
Energy Technology Data Exchange (ETDEWEB)
Su, Nan
2010-07-01
This dissertation is devoted to the study of thermodynamics for quantum gauge theories. The poor convergence of quantum field theory at finite temperature has been the main obstacle in the practical applications of thermal QCD for decades. In this dissertation I apply hard-thermal-loop perturbation theory, which is a gauge-invariant reorganization of the conventional perturbative expansion for quantum gauge theories to the thermodynamics of QED and Yang-Mills theory to three-loop order. For the Abelian case, I present a calculation of the free energy of a hot gas of electrons and photons by expanding in a power series in m{sub D}/T, m{sub f}/T and e{sup 2}, where m{sub D} and m{sub f} are the photon and electron thermal masses, respectively, and e is the coupling constant. I demonstrate that the hard-thermal-loop perturbation reorganization improves the convergence of the successive approximations to the QED free energy at large coupling, e {proportional_to} 2. For the non-Abelian case, I present a calculation of the free energy of a hot gas of gluons by expanding in a power series in m{sub D}/T and g{sup 2}, where m{sub D} is the gluon thermal mass and g is the coupling constant. I show that at three-loop order hard-thermal-loop perturbation theory is compatible with lattice results for the pressure, energy density, and entropy down to temperatures T {proportional_to} 2 - 3 T{sub c}. The results suggest that HTLpt provides a systematic framework that can be used to calculate static and dynamic quantities for temperatures relevant at LHC. (orig.)
Exact Results in Gauge Theories: Putting Supersymmetry to Work. The 1999 Sakurai Prize Lecture
Shifman, M.
1999-01-01
Powerful methods based on supersymmetry allow one to find exact solutions to certain problems in strong coupling gauge theories. The inception of some of these methods (holomorphy in the gauge coupling and other chiral parameters, in conjunction with instanton calculations) dates back to the 1980's. I describe the early exact results -- the calculation of the beta function and the gluino condensate -- and their impact on the subsequent developments. A brief discussion of the recent breakthrou...
Local existence of N=1 supersymmetric gauge theory in four Dimensions
International Nuclear Information System (INIS)
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
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.
Gravitational Goldstone fields from affine gauge theory
Tresguerres, R
2000-01-01
In order to facilitate the application of standard renormalization techniques, gravitation should be decribed, if possible, in pure connection formalism, as a Yang-Mills theory of a certain spacetime group, say the Poincare or the affine group. This embodies the translational as well as the linear connection. However, the coframe is not the standard Yang-Mills type gauge field of the translations, since it lacks the inhomogeneous gradient term in the gauge transformations. By explicitly restoring the "hidden" piece responsible for this behavior within the framework of nonlinear realizations, the usual geometrical interpretation of the dynamical theory becomes possible, and in addition one can avoid the metric or coframe degeneracy which would otherwise interfere with the integrations within the path integral. We claim that nonlinear realizations provide a general mathematical scheme clarifying the foundations of gauge theories of spacetime symmetries. When applied to construct the Yang-Mills theory of the aff...
Gravity as the Square of Gauge Theory
Bern, Zvi; Huang, Yu-tin; Kiermaier, Michael
2010-01-01
We explore consequences of the recently discovered duality between color and kinematics, which states that kinematic numerators in a diagrammatic expansion of gauge-theory amplitudes can be arranged to satisfy Jacobi-like identities in one-to-one correspondence to the associated color factors. Using on-shell recursion relations, we give a field-theory proof showing that the duality implies that diagrammatic numerators in gravity are just the product of two corresponding gauge-theory numerators, as previously conjectured. These squaring relations express gravity amplitudes in terms of gauge-theory ingredients, and are a recasting of the Kawai, Lewellen and Tye relations. Assuming that numerators of loop amplitudes can be arranged to satisfy the duality, our tree-level proof immediately carries over to loop level via the unitarity method. We then present a Yang-Mills Lagrangian whose diagrams through five points manifestly satisfy the duality between color and kinematics. The existence of such Lagrangians sugge...
Origin of gauge invariance in string theory
Horowitz, G. T.; Strominger, A.
1986-01-01
A first quantization of the space-time embedding Chi exp mu and the world-sheet metric rho of the open bosonic string. The world-sheet metric rho decouples from S-matrix elements in 26 dimensions. This formulation of the theory naturally includes 26-dimensional gauge transformations. The gauge invariance of S-matrix elements is a direct consequence of the decoupling of rho. Second quantization leads to a string field Phi(Chi exp mu, rho) with a gauge-covariant equation of motion.
Quantum communication, reference frames and gauge theory
van Enk, S. J.
2006-01-01
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communi...
Quantum communication, reference frames, and gauge theory
International Nuclear Information System (INIS)
We consider quantum communication in the case that the communicating parties not only do not share a reference frame but use imperfect quantum communication channels, in that each channel applies some fixed but unknown unitary rotation to each qubit. We discuss similarities and differences between reference frames within that quantum communication model and gauge fields in gauge theory. We generalize the concept of refbits and analyze various quantum communication protocols within the communication model
The Nonlinear Quantum Gauge Theory-Superrelativity
Leifer, Peter
1997-01-01
A new type of a nonlinear gauge quantum theory (superrelativity) has been proposed. Such theory demands a radical reconstruction of both the quantum field conception and spacetime structure, and this paves presumably way to the comprehension of the quantum nature of inertia.
Gauge theories of infinite dimensional Hamiltonian superalgebras
International Nuclear Information System (INIS)
Symplectic diffeomorphisms of a class of supermanifolds and the associated infinite dimensional Hamiltonian superalgebras, H(2M,N) are discussed. Applications to strings, membranes and higher spin field theories are considered: The embedding of the Ramond superconformal algebra in H(2,1) is obtained. The Chern-Simons gauge theory of symplectic super-diffeomorphisms is constructed. (author). 29 refs
String theory dual of the β-deformed gauge theory
International Nuclear Information System (INIS)
We consider the AdS/CFT correspondence between the β-deformed supersymmetric gauge theory and the type IIB string theory on the Lunin-Maldacena background. Guided by gauge theory results, we modify and extend the supergravity solution of Lunin and Maldacena in two ways. First we make it to be doubly periodic in the deformation parameter, β→β+1 and β→β+τ0, to match the β-periodicity property of the dual gauge theory. Secondly, we reconcile the SL(2,Z) symmetry of the gauge theory, which acts on the constant parameters τ0 and β, with the SL(2,Z) invariance of the string theory, which involves the dilaton-axion field τ(x). Our proposed modified configuration transforms correctly under the SL(2,Z) of string theory when its parameters are transformed under the SL(2,Z) of the gauge theory. We interpret the resulting configuration as the string theory (rather than supergravity) background which is dual to the β-deformed conformal Yang-Mills. Finally, we check that our string theory background leads to the IIB effective action which is correctly reproduced by instanton calculations on the gauge theory side, carried out at weak coupling, in the large-N limit, but to all orders in the deformation parameter β
Chiral symmetry and chiral-symmetry breaking
International Nuclear Information System (INIS)
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed
Experimental tests of gauge theories
International Nuclear Information System (INIS)
This series of five lectures is intended to provide the experimental basis to the theoretical courses on gauge symmetries. The framework is the standard model. The experimental material is taken mainly from lepton-hadron and e+e--experiments. Choosing the Standard Model as framework offers the possibility of a simple and organized presentation of the rich material. The other advantage of the present form of the standard model concerns the formulation of the critical questions leading beyond the tested ground, for instance why are weak interactions lefthanded or is the multitude of quarks and leptons hinting at yet another substructure. (orig./HSI)
An ultraviolet chiral theory of the top for the fundamental composite (Goldstone) Higgs
Giacomo Cacciapaglia; Francesco Sannino(Syracuse Univ., Univ. ``Federico II'' & INFN)
2016-01-01
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also ...
Lattice study for conformal windows of SU(2) and SU(3) gauge theories with fundamental fermions
Huang, Cynthia Y -H; Lin, C -J David; Ogawa, Kenji; Ohki, Hiroshi; Ramos, Alberto; Rinaldi, Enrico
2015-01-01
We present our investigation of SU(2) gauge theory with 8 flavours, and SU(3) gauge theory with 12 flavours. For the SU(2) case, at strong bare coupling, $\\beta \\lesssim 1.45$, the distribution of the lowest eigenvalue of the Dirac operator can be described by chiral random matrix theory for the Gaussian symplectic ensemble. Our preliminary result indicates that the chiral phase transition in this theory is of bulk nature. For the SU(3) theory, we use high-precision lattice data to perform the step-scaling study of the coupling, $g_{{\\rm GF}}$, in the Gradient Flow scheme. We carefully examine the reliability of the continuum extrapolation in the analysis, and conclude that the scaling behaviour of this SU(3) theory is not governed by possible infrared conformality at $g_{{\\rm GF}}^{2} \\lesssim 6$.
Chiral unitary theory: Application to nuclear problems
Indian Academy of Sciences (India)
E Oset; D Cabrera; H C Chiang; C Garcia Recio; S Hirenzaki; S S Kamalov; J Nieves; Y Okumura; A Ramos; H Toki; M J Vicente Vacas
2001-08-01
In this talk we brieﬂy describe some basic elements of chiral perturbation theory, , and how the implementation of unitarity and other novel elements lead to a better expansion of the -matrix for meson–meson and meson–baryon interactions. Applications are then done to the interaction in nuclear matter in the scalar and vector channels, antikaons in nuclei and - atoms, and how the meson properties are changed in a nuclear medium.
Quantum geometry and quiver gauge theories
Nekrasov, Nikita; Shatashvili, Samson
2013-01-01
We study macroscopically two dimensional $\\mathcal{N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\\mathbb{T}^{d} \\times \\mathbb{R}^{2}_{\\epsilon}$ of a $d$-dimensional torus and a two dimensional cigar with $\\Omega$-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on $\\mathbb{R}^{2-d} \\times \\mathbb{T}^{2+d}$ and singular monopoles on $\\mathbb{R}^{2-d} \\times \\mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian $\\mathbf{Y}_{\\epsilon}(\\mathfrak{g}_{\\Gamma})$, quantum affine algebra $\\mathbf{U}^{\\mathrm{aff}}_q(\\mathfrak{g}_{\\Gamma})$, or the quantum elliptic algebra $\\mathbf{U}^{\\mathrm{ell}}_{q,p}(\\mathfrak{g}_{\\Gamma})$ associated to Kac-Moody algebra $\\mathfrak{g}_{\\Gamma}$ for quiver $\\Gamma$.
de Sitter gauge theories and induced gravities
International Nuclear Information System (INIS)
Pure de Sitter, anti de Sitter, and orthogonal gauge theories in four-dimensional Euclidean spacetime are studied. It is shown that, if the theory is asymptotically free and a dynamical mass is generated, then an effective geometry may be induced and a gravity theory emerges. The asymptotic freedom and the running of the mass might account for an Inoenue-Wigner contraction which induces a breaking of the gauge group to the Lorentz group, while the mass itself is responsible for the coset sector of the gauge field to be identified with the effective vierbein. Furthermore, the resulting local isometries are Lorentzian for the anti de Sitter group and Euclidean for the de Sitter and orthogonal groups. (orig.)
Matrix product states for lattice gauge theories
International Nuclear Information System (INIS)
Gauge theories hold a most prominent place in physics: not only do they lie at the root of the standard model, but they appear as low-energy theories in condensed matter. We focus on (1+1)-D QED aka the Schwinger model. This toy-model shares some interesting features with QCD like for instance the confinement. We show how matrix product states can be used to efficiently simulate equilibrium and non-equilibrium physics in a gauge invariant way. In particular, we approximate the ground state, determine particle-like excitations, investigate confinement and study real-time evolution with a global quench. We also discuss how this ideas can be generalised to non-abelian gauge theories and/or higher dimensions. References: [1] arXiv:1312.6654 [hep-lat] [2] arXiv:1411.0020 [hep-lat] (author)
Renormalization of gauge theories without cohomology
Anselmi, Damiano
2013-07-01
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem.
Renormalization of gauge theories without cohomology
Energy Technology Data Exchange (ETDEWEB)
Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa (Italy)
2013-07-15
We investigate the renormalization of gauge theories without assuming cohomological properties. We define a renormalization algorithm that preserves the Batalin-Vilkovisky master equation at each step and automatically extends the classical action till it contains sufficiently many independent parameters to reabsorb all divergences into parameter-redefinitions and canonical transformations. The construction is then generalized to the master functional and the field-covariant proper formalism for gauge theories. Our results hold in all manifestly anomaly-free gauge theories, power-counting renormalizable or not. The extension algorithm allows us to solve a quadratic problem, such as finding a sufficiently general solution of the master equation, even when it is not possible to reduce it to a linear (cohomological) problem. (orig.)
Curving Yang-Mills-Higgs Gauge Theories
Kotov, Alexei
2015-01-01
Established fundamental physics can be described by fields, which are maps. The source of such a map is space-time, which can be curved due to gravity. The map itself needs to be curved in its gauge field part so as to describe interaction forces like those mediated by photons and gluons. In the present article, we permit non-zero curvature also on the internal space, the target of the field map. The action functional and the symmetries are constructed in such a way that they reduce to those of standard Yang-Mills-Higgs (YMH) gauge theories precisely when the curvature on the target of the fields is turned off. For curved targets one obtains a new theory, a curved YMH gauge theory. It realizes in a mathematically consistent manner an old wish in the community: replacing structures constants by functions depending on the scalars of the theory. In addition, we provide a simple 4d toy model, where the gauge symmetry is abelian, but turning off the gauge fields, no rigid symmetry remains---another possible manife...
Local Poincaré Symmetry in Gauge Theory of Gravity
Institute of Scientific and Technical Information of China (English)
MA Jian-Feng; MA Yong-Ge
2009-01-01
It is well known that the Poincaré gauge theories of gravity do not have the structure of a standard gauge theory. Nevertheless, we show that a general form of action for the gravitational gauge fields in the gauge theory does possess local Poincaré invariance.
A gauge theory of massive spin one particles
Vyas, Vivek M
2015-01-01
An Abelian gauge theory describing dynamics of massive spin one bosons is constructed. This is achieved by appending to the Maxwell action, a gauge invariant mass term. The theory is quantised in temporal as well as Lorentz gauge, and the corresponding Hilbert spaces are constructed. In both the gauges, it is found that, the theory respects Lorentz invariance, locality, causality and unitarity.
Closed string field theory in a-gauge
Asano, Masako; Kato, Mitsuhiro
2012-01-01
We show that a-gauge, a class of covariant gauges developed for bosonic open string field theory, is consistently applied to the closed string field theory. A covariantly gauge-fixed action of massless fields can be systematically derived from a-gauge-fixed action of string field theory.
Link homology and equivariant gauge theory
Poudel, Prayat; Saveliev, Nikolai
2015-01-01
The singular instanton Floer homology was defined by Kronheimer and Mrowka in connection with their proof that the Khovanov homology is an unknot detector. We study this theory for knots and two-component links using equivariant gauge theory on their double branched covers. We show that the special generator in the singular instanton Floer homology of a knot is graded by the knot signature mod 4, thereby providing a purely topological way of fixing the absolute grading in the theory. Our appr...
On novel string theories from 4d gauge theories
Directory of Open Access Journals (Sweden)
Kiritsis Elias
2014-04-01
Full Text Available We investigate strings theories as defined from four dimensional gauge theories. It is argued that novel (superstring theories exist up to 26 dimensions. Some of them may support weakly curved geometries. A proposal is outlined to link their local conformal invariance to the dynamics of the bulk string theory.
Aspects of entanglement entropy for gauge theories
Soni, Ronak M.; Trivedi, Sandip P.
2016-01-01
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-01-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a non-equilibrium transformation of a system, to the free-energy difference between two equilibrium states. In this article, we extend Jarzynski's theorem to lattice gauge theory, and present examples of applications for two challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schroedinger functional and for simulations at finite density using reweighting techniques.
Jarzynski's theorem for lattice gauge theory
Caselle, Michele; Costagliola, Gianluca; Nada, Alessandro; Panero, Marco; Toniato, Arianna
2016-08-01
Jarzynski's theorem is a well-known equality in statistical mechanics, which relates fluctuations in the work performed during a nonequilibrium transformation of a system, to the free-energy difference between two equilibrium ensembles. In this article, we apply Jarzynski's theorem in lattice gauge theory, for two examples of challenging computational problems, namely the calculation of interface free energies and the determination of the equation of state. We conclude with a discussion of further applications of interest in QCD and in other strongly coupled gauge theories, in particular for the Schrödinger functional and for simulations at finite density using reweighting techniques.
Gauge-Invariant Formalism with Dirac-mode Expansion for Confinement and Chiral Symmetry Breaking
Gongyo, Shinya; Suganuma, Hideo
2012-01-01
We develop a manifestly gauge-covariant expansion of the QCD operator such as the Wilson loop, using the eigen-mode of the QCD Dirac operator $\\Slash D=\\gamma^\\mu D^\\mu$. With this method, we perform a direct analysis of the correlation between confinement and chiral symmetry breaking in lattice QCD Monte Carlo calculation on $6^4$ at $\\beta$=5.6. As a remarkable fact, the confinement force is almost unchanged even after removing the low-lying Dirac modes, which are responsible to chiral symmetry breaking. This indicates that one-to-one correspondence does not hold for between confinement and chiral symmetry breaking in QCD. In this analysis, we carefully amputate only the "essence of chiral symmetry breaking" by cutting off the low-lying Dirac modes, and can artificially realize the "confined but chiral restored situation" in QCD.
National Computational Infrastructure for Lattice Gauge Theory
Energy Technology Data Exchange (ETDEWEB)
Brower, Richard C.
2014-04-15
SciDAC-2 Project The Secret Life of Quarks: National Computational Infrastructure for Lattice Gauge Theory, from March 15, 2011 through March 14, 2012. The objective of this project is to construct the software needed to study quantum chromodynamics (QCD), the theory of the strong interactions of sub-atomic physics, and other strongly coupled gauge field theories anticipated to be of importance in the energy regime made accessible by the Large Hadron Collider (LHC). It builds upon the successful efforts of the SciDAC-1 project National Computational Infrastructure for Lattice Gauge Theory, in which a QCD Applications Programming Interface (QCD API) was developed that enables lattice gauge theorists to make effective use of a wide variety of massively parallel computers. This project serves the entire USQCD Collaboration, which consists of nearly all the high energy and nuclear physicists in the United States engaged in the numerical study of QCD and related strongly interacting quantum field theories. All software developed in it is publicly available, and can be downloaded from a link on the USQCD Collaboration web site, or directly from the github repositories with entrance linke http://usqcd-software.github.io
Experimental tests of gauge theories
International Nuclear Information System (INIS)
The author reviews the experimental tests of the Weinberg-Salam theory, quantum chromodynamics, and grand unified theories. These are studies of the V-A behaviour of weak charged currents, studies of weak neutral currents by measurement of parity violating asymmetries with special regards to deep inelastic ed scattering, neutrino-induced neutral-current interactions, charge asymmetry in deep inelastic muon scattering, and #betta#-Z interference in e+e--annihilation, which are related to the Weinberg-Salam theory, measurements of structure functions in deep inelastic scattering and jet studies in e+e--annihilation and inclusive hadronic processes which are related to quantum chromodynamics, and as tests of grand unified theories measurements of the proton decay. (HSI)
Concise theory of chiral lipid membranes
Tu, Z C
2007-01-01
A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \\textit{et al.}, Science \\textbf{264}, 945 (1994); M.S. Spector \\textit{et al.}, Langmuir \\textbf{14}, 3493 (1998); Y. Zhao, \\textit{et al.}, Proc. Natl. Acad. Sci. USA \\textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\\circ$ and 35$^\\circ$, which are close to the mo...
Local subsystems in gauge theory and gravity
Donnelly, William
2016-01-01
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of space. We present a general formalism to associate a gauge-invariant classical phase space to a spatial slice with boundary by introducing new degrees of freedom on the boundary. In Yang-Mills theory the new degrees of freedom are a choice of gauge on the boundary, transformations of which are generated by the normal component of the nonabelian electric field. In general relativity the new degrees of freedom are the location of a codimension-2 surface and a choice of conformal normal frame. These degrees of freedom transform under a group of surface symmetries, consisting of diffeomorphisms of the codimension-2 boundary, and position-dependent linear deformations of its normal plane. We find the observables which generate these symmetries, consisting of the conformal normal me...
Supersymmetric gauge theories, vortices and equivariant cohomology
Energy Technology Data Exchange (ETDEWEB)
Machin, W; Papadopoulos, G [Department of Mathematics, King' s College London, Strand, London WC2R 2LS (United Kingdom)
2003-04-07
We construct actions for (p, 0)- and (p, 1)-supersymmetric, 1 {<=} p {<=} 4, two-dimensional gauge theories coupled to nonlinear sigma model matter with a Wess-Zumino term. We derive the scalar potential for a large class of these models. We then show that the Euclidean actions of the (2, 0)- and (4, 0)-supersymmetric models without Wess-Zumino terms are bounded by topological charges which involve the equivariant extensions of the Kaehler forms of the sigma model target spaces evaluated on the two-dimensional spacetime. We give similar bounds for Euclidean actions of appropriate gauge theories coupled to nonlinear sigma model matter in higher spacetime dimensions which now involve the equivariant extensions of the Kaehler forms of the sigma model target spaces and the second Chern character of gauge fields. The BPS configurations are generalizations of Abelian and non-Abelian vortices.
Chiral dynamics in U(3) unitary chiral perturbation theory
International Nuclear Information System (INIS)
We perform a complete one-loop calculation of meson-meson scattering, and of the scalar and pseudoscalar form factors in U(3) chiral perturbation theory with the inclusion of explicit resonance fields. This effective field theory takes into account the low-energy effects of the QCD UA(1) anomaly explicitly in the dynamics. The calculations are supplied by non-perturbative unitarization techniques that provide the final results for the meson-meson scattering partial waves and the scalar form factors considered. We present thorough analyses on the scattering data, resonance spectroscopy, spectral functions, Weinberg-like sum rules and semi-local duality. The last two requirements establish relations between the scalar spectrum with the pseudoscalar and vector ones, respectively. The NC extrapolation of the various quantities is studied as well. The fulfillment of all these non-trivial aspects of the QCD dynamics by our results gives a strong support to the emerging picture for the scalar dynamics and its related spectrum.
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
International Nuclear Information System (INIS)
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of UA(1) symmetry and the η' for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk
Fermion frontiers in vector lattice gauge theories: Proceedings. Volume 8
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-11-01
The inclusion of fermions into simulations of lattice gauge theories is very difficult both theoretically and numerically. With the presence of Teraflops-scale computers for lattice gauge theory, the authors wanted a forum to discuss new approaches to lattice fermions. The workshop concentrated on approaches which are ripe for study on such large machines. Although lattice chiral fermions are vitally important to understand, there is not technique at hand which is viable on these Teraflops-scale machines for real-world problems. The discussion was therefore focused on recent developments and future prospects for QCD-like theories. For the well-known fermion formulations, the Aoki phase in Wilson fermions, novelties of U{sub A}(1) symmetry and the {eta}{prime} for staggered fermions and new approaches for simulating the determinant for Wilson fermions were discussed. The newer domain-wall fermion formulation was reviewed, with numerical results given by many speakers. The fermion proposal of Friedberg, Lee and Pang was introduced. They also were able to compare and contrast the dependence of QCD and QCD-like SUSY theories on the number of quark flavors. These proceedings consist of several transparencies and a summary page from each speaker. This should serve to outline the major points made in each talk.
Topologically Massive Gauge Theory: A Lorentzian Solution
Saygili, K
2006-01-01
We obtain a lorentzian solution for the topologically massive non-abelian gauge theory on AdS space by means of a SU(1, 1) gauge transformation of the previously found abelian solution. There exists a natural scale of length which is determined by the inverse topological mass. The topological mass is proportional to the square of the gauge coupling constant. In the topologically massive electrodynamics the field strength locally determines the gauge potential up to a closed 1-form via the (anti-)self-duality equation. We introduce a transformation of the gauge potential using the dual field strength which can be identified with an abelian gauge transformation. Then we present the map from the AdS space to the pseudo-sphere including the topological mass. This is the lorentzian analog of the Hopf map. This map yields a global decomposition of the AdS space as a trivial circle bundle over the upper portion of the pseudo-sphere which is the the Hyperboloid model for the Lobachevski geometry. This leads to a redu...
Stochastic field theory for a Dirac particle propagating in gauge field disorder
Guhr, T; Weidenmüller, H A
2000-01-01
Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.
Space-time dependent couplings In N = 1 SUSY gauge theories: Anomalies and central functions
International Nuclear Information System (INIS)
We consider N = 1 supersymmetric gauge theories in which the couplings are allowed to be space-time dependent functions. Both the gauge and the superpotential couplings become chiral superfields. As has recently been shown, a new topological anomaly appears in models with space-time dependent gauge coupling. Here we show how this anomaly may be used to derive the NSVZ β-function in a particular, well-determined renormalisation scheme, both without and with chiral matter. Moreover we extend the topological anomaly analysis to theories coupled to a classical curved superspace background, and use it to derive an all-order expression for the central charge c, the coefficient of the Weyl tensor squared contribution to the conformal anomaly. We also comment on the implications of our results for the central charge a expected to be of relevance for a four-dimensional C-theorem. (author)
Compositeness Condition for Dynamically Induced Gauge Theories
Akama, K; Akama, Keiichi; Hattori, Takashi
1997-01-01
We show that the compositeness condition for the induced gauge boson in the four-fermion interaction theory actually works beyond the one-loop approximation. The next-to-leading contributions are calculated, and turn out to be reasonably suppressed, so that the leading-order approximation is justified.
Hot gauge theories in external electromagnetic fields
International Nuclear Information System (INIS)
A general treatment of finite temperature and external electromagnetic field effects for gauge theories is presented. The results are illustrated explicitly for the SU(2) model of Georgi and Glashow, for which we obtain the finite temperature one-loop effective action in the presence of an external magnetic field. We discuss briefly the possible use of the results obtained. (author)
Gauged Supergravity and Holographic Field Theory
Warner, Nicholas P.
2002-01-01
This is a slightly expanded version of my talk at Future Perspectives in Theoretical Physics and Cosmology, Stephen Hawking's 60th Birthday Worshop. I describe some of the issues that were important in gauged supergravity in the 1980's and how these, and related issues have once again become important in the study of holographic field theories.
Domain wall fermions in vector gauge theories
Blum, T.
1998-01-01
I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum, weak matrix elements, the $n_f=2$ finite temperature phase transition, and topology and zero modes and conclude with topics for future study.
Pauli-Guersey symmetry in gauge theories
International Nuclear Information System (INIS)
Gauge theories with massless or massive fermions in a selfcontragredient representation exhibit global symmetries of Pauli-Guersey type. Some of them are broken spontaneously leading to a difermion Goldstone bosons. An example of a boson version of the Pauli-Guersey symmetry is provided by the Weinberg-Salam model in the limit THETAsub(w)→O
Extended monopoles in gauge field theories
International Nuclear Information System (INIS)
The paper gives a review of the 't Hooft monopole and briefly discusses the general topological considerations connected with monopoles. A method is presented for constructing explicit monopole solutions in any gauge theory. Some stability questions and time-dependent problems are also considered
Some properties of renormalons in gauge theories
Di Cecio, G
1994-01-01
We find the explicit operatorial form of renormalon-type singularities in abelian gauge theory. Local operators of dimension six take care of the first U.V. renormalon, non local operators are needed for I.R. singularities. In the effective lagrangian constructed with these operators non local imaginary parts appearing in the usual perturbative expansion at large orders are cancelled.
Recent advances in lattice gauge theories
Indian Academy of Sciences (India)
R V Gavai
2000-04-01
Recent progress in the ﬁeld of lattice gauge theories is brieﬂy reviewed for a nonspecialist audience. While the emphasis is on the latest and more deﬁnitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.
An effective theory of massive gauge bosons
International Nuclear Information System (INIS)
The coupling of a group-valued massive scalar field to a gauge field through a symmetric rank-2 field strenght is studied. By considering energies very small compared with the mass of the scalar and invoking the decoupling theorem, one is left with a low-energy effective theory describing a dynamics of massive vector fields. (Author)
Witten index calculation in supersymmetric gauge theory
International Nuclear Information System (INIS)
Direct calculation of the Witten index Isub(W) in the SU(2) SUSY Yang-Mills theiory is performed using the periodic boundary conditions. Our result is Isub(W)--1 which disagrees with the Witten's result: Isub(W)=N for the SU(N) gauge group. The principle physical conclusion of SUSY unbreaking in this theory remains intact
Chiral heat wave and mixed waves in kinetic theory
Frenklakh, D
2016-01-01
We study collective excitations in hot rotating chiral media in presence of magnetic field in kinetic theory, namely Chiral Heat Wave and its' mixings with Chiral Vortical Wave and Chiral Magnetic Wave. Our results for velocities of these waves have slight alterations from those obtained earlier. We explain the origin of these alterations and also give the most general expressions for the velocities of all these waves in hydrodynamic approach.
Perturbative gauge theory in a background
Dietrich, D D; Peigné, S; Dietrich, Dennis D.; Hoyer, Paul; Jarvinen, Matti; Peigne, Stephane
2007-01-01
Motivated by the gluon condensate in QCD we study the perturbative expansion of a gauge theory in the presence of gauge bosons of vanishing momentum, in the specific case of an abelian theory. The background is characterised by a dimensionful parameter $\\Lambda$ affecting only the on-shell prescription of the free (abelian) gluon propagator. When summed to all orders in $g\\Lambda$ the modification is equivalent to evaluating standard Green functions in a pure gauge field with an imaginary gauge parameter $\\propto \\Lambda$. We show how to calculate the corresponding dressed Green functions, which are Poincar\\'e and gauge covariant. We evaluate the expressions for the dressed quark and $q \\bar q$ propagators, imposing as boundary condition that they approach the standard perturbative form in the short-distance limit ($|p^2|\\to\\infty$). The on-shell ($p^2=m^2$) pole of the free quark propagator is removed for any $\\Lambda > 0$, and replaced by a discontinuity which vanishes exponentially with $p^2$. The dressing...
Field strength formulation of gauge theories
International Nuclear Information System (INIS)
In this thesis an alternative to the usual formulation of gauge theories is presented. The usual description in terms of vector field potentials A/sub μ/(x) is replaced by a description in terms of field strength tensors Fμ/sub v/(x). This is done in the coordinate gauge, xμA/sub μ/(x) = 0, where the vector potentials can be expressed in a simple form in terms of the field strengths. The inversion formula gives a one-to-one correspondence between smooth fields A/sub μ/ and F/sub μv/. Even for singular A/sub μ/ configurations, it has been shown that the set of potentials which corresponds to the same F/sub μv/ (copies) is probably of measure zero in the space of potentials. Furthermore, the field strength tensor in the coordinate gauge has to satisfy the Bianchi identities. As a result the generating functional Z[J] for the quantum field theory may be transformed from an expression in terms of Aμ(x) to one in terms of fields lambda(sub sigma)x can be introduced to enforce these constraints. The tensor fields F/sub μv/(x). The Bianchi identities appear as constraints on the allowed class of tensors F/sub μv(x). A set of Lagrange multiplier fields lambda/sub sigma/(x) can be introduced to enforce these constraints. The tensor fields F/sub μv/(x) can be integrated out in the functional integral for Z, leaving an expression for Z[J] in terms of the fields lambdasigma(x). This appears to be useful for analyzing the strong coupling limit of the gauge theory. Our results are closely related to, but are much simpler than, Halpern's dual variable formulation of gauge theories in the axial gauge. The Hamiltonian formalism for systems with constraints corresponding to this field strength formulation was also developed for the abelian theory. The results show that the field strength formulation of the gauge theory can be seen as defining a new quantum theory in its own right
Göckeler, M; Rakow, P E L; Schäfer, A; Wettig, T
2002-01-01
We calculate complete spectra of the Kogut-Susskind Dirac operator on the lattice in quenched SU(3) gauge theory for various values of coupling constant and lattice size. From these spectra we compute the connected and disconnected scalar susceptibilities and find agreement with chiral random matrix theory up to a certain energy scale, the Thouless energy. The dependence of this scale on the lattice volume is analyzed. In the case of the connected susceptibility this dependence is anomalous, and we explain the reason for this. We present a model of chiral perturbation theory that is capable of describing the data beyond the Thouless energy and that has a common range of applicability with chiral random matrix theory.
More Arnold's N = 2 superconformal gauge theories
Del Zotto, Michele
2011-01-01
We study the N = 2 gauge theories obtained by engineering the Type IIB superstring on the quasi-homogeneous elements of Arnold's list of bimodal singularities. All these theories have finite BPS chambers and we describe, along the lines of [arXiv:1107.5747], the algebraically obvious ones. Our results leads to the prediction of 11 new periodic Y-systems, providing additional evidence for the correspondence in between thermodinamical Bethe ansatz periodic Y-systems and N = 2 superconformal the...
Large transverse momentum behavior of gauge theories
International Nuclear Information System (INIS)
The large transverse momentum behavior of Compton scattering and Moeller scattering in Quantum Electrodynamics; and of elastic quark-quark scattering in Quantum Chromodynamics are examined in perturbation theory. The results strongly suggest that the large transverse momentum regime in gauge theories is governed by a differential equation of the Callan-Symanzik type with a suitable momentum dependent anomalous dimension term. An explicit solution for the quark-quark elastic scattering amplitude at large transverse momentum is given
Effects of gauge boson mass on chiral and deconfinement phase transitions in QED$_{3}$
Yin, Pei-Lin; Feng, Hong-Tao; Zong, Hong-Shi
2016-01-01
Based on the experimental observation that there is a coexisting region between the antiferromagnetic (AF) and $\\textit{d}$-wave superconducting ($\\textit{d}$SC) phases, the influences of gauge boson mass $m_{a}$ on chiral symmetry restoration and deconfinement phase transitions in QED$_{3}$ are investigated simultaneously within a unified framework, i.e., Dyson-Schwinger equations. The results show that the chiral symmetry restoration phase transition in the presence of the gauge boson mass $m_{a}$ is a typical second-order phase transition; the chiral symmetry restoration and deconfinement phase transitions are coincident; the critical number of fermion flavors $N^{c}_{f}$ decreases as the gauge boson mass $m_{a}$ increases and there exists a boundary that separates the $N^{c}_{f}$-$m_{a}$ plane into chiral symmetry breaking/confinement region for ($N_{f}^{c}$, $m_{a}$) below the boundary and chiral symmetry restoration/deconfinement region for ($N_{f}^{c}$, $m_{a}$) above it.
Radiative effects in gauge theories
Borisov, A. V.; Zhukovskii, V. Ch.
1987-10-01
The definitions of the vacuum state and the analysis of the radiative processes reffer to fundamental problems of non-abelian gayge theories. On the basis of the functional integration in the proper time representation a model of vacuum is examined of the quantum chromodynamics, proposed by Savvidy and Matinyan (Nuclear Physics B, Volume 134, Issue 3, p. 539-545). The supersimmetry of the Dirac equation for fermions in an external constant homogeneous magnetic field is examined. The radiative shift is calculated for the Dirac neutrino mass in an arbitrary external constant electromagnetic field in the framework of the Weinberg-Salam theory. An interpretation of the sign of the neutrino's anomalous magnetic moment is given. The power of the electromagnetic radiation of the moment and characteristic time of the neutrino spirality flipp in an external magnetic field is calculated. Bibliography: 24; Ill. 2
Energy Technology Data Exchange (ETDEWEB)
Knecht, M. [Paris-11 Univ., 91 - Orsay (France). Inst. de Physique Nucleaire
1996-12-31
Chiral perturbation theory enables to link some hadronic processes at low energy involving {pi},K and {eta} pseudo scalar mesons with some non-perturbative QCD observables which reflect chiral symmetry breaking. The possibilities of investigating the chiral structure of QCD emptiness in several experimental projects within the field of hadronic physics are reviewed 44 refs.
Fundamental problems of gauge field theory
International Nuclear Information System (INIS)
As a result of the experimental and theoretical developments of the last two decades, gauge field theory, in one form or another, now provides the standard language for the description of Nature; QCD and the standard model of the electroweak interactions illustrate this point. It is a basic task of mathematical physics to provide a solid foundation for these developments by putting the theory in a physically transparent and mathematically rigorous form. The lecture notes collected in this volume concentrate on the many unsolved problems which arise here, and on the general ideas and methods which have been proposed for their solution. In particular, the use of rigorous renormalization group methods to obtain control over the continuum limit of lattice gauge field theories, the exploration of the extraordinary enigmatic connections between Kac-Moody-Virasoro algebras and string theory, and the systematic use of the theory of local algebras and indefinite metric spaces to classify the charged C* states in gauge field theories are mentioned
High energy behaviour of nonabelian gauge theories
International Nuclear Information System (INIS)
The high energy behavior (in the Regge limit) of nonabelian gauge theories is reviewed. After a general remark concerning the question to what extent the Regge limit can be approached within perturbation theory, we first review the reggeization of elementary particles within nonabelian gauge theories. Then the derivation of a unitary high energy description of a massive (= spontaneously broken) nonabelian gauge model is described, which results in a complete reggeon calculus. There is strong evidence that the zero mass limit of this reggeon calculus exists, thus giving rise to the hope that the Regge behavior in pure Yang-Mills theories (QCD) can be reached in this way. In the final part of these lectures two possible strategies for solving this reggeon calculus (both for the massive and the massless case) are outlined. One of them leads to a geometrical picture in which the distribution of the wee partons obeys a diffusion law. The other one makes contact with reggeon field theory and predicts that QCD in the high energy limit is described by critical reggeon field theory. (orig.)
New Chiral Fermions, a New Gauge Interaction, Dirac Neutrinos, and Dark Matter
de Gouvea, André
2015-01-01
We propose that all light fermionic degrees of freedom, including the Standard Model (SM) fermions and all possible light beyond-the-standard-model fields, are chiral with respect to some spontaneously broken abelian gauge symmetry. Hypercharge, for example, plays this role for the SM fermions. We introduce a new symmetry, $U(1)_{\
A U(1) gauge theory for anyons
International Nuclear Information System (INIS)
A U(1) gauge theory of a particle with arbitrary spin in three space-time dimensions is introduced. All the spin-dependent effects are a consequence of a direct coupling of the gauge field to the Chern-Simons field responsible for the shift in spin and statistics. Two approaches in relativistic quantum mechanics which take a spin-0 or a spin-1/2 state as starting point are shown to be equivalent and the result is that the total spin dependence reduces to a magnetic coupling with a gyromagnetic ratio g=2 for any spin. (orig.)
Cosmic string in compactified gauge theory
International Nuclear Information System (INIS)
A solution of the vortex type is given in a six-dimensional SU(2)xU(1) pure gauge theory coupled to Einstein gravity in a compactified background geometry. We construct the solution of an effective Abelian-Higgs model in terms of dimensional reduction. The solution, however, has a peculiarity in its physically relevant quantity, a deficit angle, which is given as a function of the ratio of the gauge couplings of SU(2) and U(1). The size of the extra space (sphere) is shown to vary with the distance from the axis of the 'string'. (author)
General Poincar\\'e Gauge Theory Cosmology
Ho, Fei-Hung; Nester, James M; Yo, Hwei-Jang
2015-01-01
For the quadratic Poincar\\'e gauge theory of gravity (PG) we consider the FLRW cosmologies using an isotropic Bianchi representation. Here the considered cosmologies are for the general case: all the even and odd parity terms of the quadratic PG with their respective scalar and pseudoscalar parameters are allowed with no \\emph{a priori} restrictions on their values. With the aid of a manifestly homogeneous and isotropic representation, an effective Lagrangian gives the second order dynamical equations for the gauge potentials. An equivalent set of first order equations for the observables is presented. The generic behavior of physical solutions is discussed and illustrated using numerical simulations.
International Nuclear Information System (INIS)
The geometrical condition of soul-flatness needed in the superfield approach to quantized gauge theories and extended BRS transformations, is derived from a lagrangian theory on a superspace Ssup(4,2). Invariance of the superlagrangian and the lagrangian of quantized gauge theories under Sp(2, R) and hermitian conjugation is discussed in different gauges. (orig.)
Quantum critical behavior of semisimple gauge theories
Esbensen, Jacob Kamuk; Ryttov, Thomas A.; Sannino, Francesco
2016-02-01
We study the perturbative phase diagram of semisimple fermionic gauge theories resembling the Standard Model. We investigate an S U (N ) gauge theory with M Dirac flavors where we gauge first an S U (M )L and then an S U (2 )L⊂S U (M )L of the original global symmetry S U (M )L×S U (M )R×U (1 ) of the theory. To avoid gauge anomalies we add leptonlike particles. At the two-loop level an intriguing phase diagram appears. We uncover phases in which one, two or three fixed points exist and discuss the associated flows of the coupling constants. We discover a phase featuring complete asymptotic freedom and simultaneously an interacting infrared fixed point in both couplings. The analysis further reveals special renormalization group trajectories along which one coupling displays asymptotic freedom and the other asymptotic safety, while both flowing in the infrared to an interacting fixed point. These are safety free trajectories. We briefly sketch out possible phenomenological implications, among which an independent way to generate near-conformal dynamics à la walking is investigated.
Hamiltonian dynamics of gauge theories of gravity
International Nuclear Information System (INIS)
We investigate the Hamiltonian structure of gauge theories of gravity based on arbitrary gravitational and matter field Lagrangians. The gauge group of the theory in question is the semisimple product of the local Lorentz group and the group of diffeomorphisms of spacetime (the local Poincare group). We derive formulas for the symplectic two-form Ω, the translational E, and the rotational J generators. The Hamilton equations expressed in terms of Ω, E, and J are equivalent to the variational Euler-Lagrange equations. The ten constraint equations of the theory are closely related both to properties of the symplectic two-form Ω and to an action of the gauge group in the space of solutions. The dynamical generators E and J can be expressed by the left-hand sides of the constraint equations, that is, the constraints generate the dynamics by means of the Hamilton equations for the functions E and J. On the other hand, the action of the gauge group in the set of initial data determines their ''time'' evolution. We show that this evolution is in a one-to-one correspondence with that generated by the Hamilton equations
Anomalous Chiral Superfluidity
Lublinsky, Michael(Physics Department, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel); Zahed, Ismail
2009-01-01
We discuss both the anomalous Cartan currents and the energy-momentum tensor in a left chiral theory with flavour anomalies as an effective theory for flavored chiral phonons in a chiral superfluid with the gauged Wess-Zumino-Witten term. In the mean-field (leading tadpole) approximation the anomalous Cartan currents and the energy momentum tensor take the form of constitutive currents in the chiral superfluid state. The pertinence of higher order corrections and the Adler-Bardeen theorem is ...
Gravity as the Square of Gauge Theory
Kiermaier, M.
The BCJ squaring relations provide a simple prescription for thecomputation of gravity amplitudes in terms of gauge theory ingredients. Unlike the KLT relations, the squaring relations are directly applicable both at tree and loop level. We review the derivation of these relations from on-shell recursion relations, and discuss an off-shell approach to these relations in which the interactions of the gravity Lagrangian arise as the square of the gauge-theory interactions. This article is based on work with Zvi Bern, Tristan Dennen and Yu-tin Huang [Z. Bern, T. Dennen, Y.-t. Huang and M. Kiermaier, Phys. Rev. D textbf{82} (2010), 065003, arXiv:1004.0693 (Ref. 1))] which was presented at String Field Theory and Related Aspects 2010.
Integrability in N=2 superconformal gauge theorie
Energy Technology Data Exchange (ETDEWEB)
Pomoni, Elli [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany). Theory Group; National Technical Univ. of Athens (Greece). Physics Div.
2013-10-15
Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1 vertical stroke 2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1 vertical stroke 2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.
Integrability in N=2 superconformal gauge theories
International Nuclear Information System (INIS)
Any N=2 superconformal gauge theory (including N=4 SYM) contains a set of local operators made only out of fields in the N=2 vector multiplet that is closed under renormalization to all loops, namely the SU(2,1 vertical stroke 2) sector. For planar N=4 SYM the spectrum of local operators can be obtained by mapping the problem to an integrable model (a spin chain in perturbation theory), in principle for any value of the coupling constant. We present a diagrammatic argument that for any planar N=2 superconformal gauge theory the SU(2,1 vertical stroke 2) Hamiltonian acting on infinite spin chains is identical to all loops to that of N=4 SYM, up to a redefinition of the coupling constant. Thus, this sector is integrable and anomalous dimensions can be, in principle, read off from the N=4 ones up to this redefinition.
Planar Zeros in Gauge Theories and Gravity
Jimenez, Diego Medrano; Vazquez-Mozo, Miguel A
2016-01-01
Planar zeros are studied in the context of the five-point scattering amplitude for gauge bosons and gravitons. In the case of gauge theories, it is found that planar zeros are determined by an algebraic curve in the projective plane spanned by the three stereographic coordinates labelling the direction of the outgoing momenta. This curve depends on the values of six independent color structures. Considering the gauge group SU(N) with N=2,3,5 and fixed color indices, the class of curves obtained gets broader by increasing the rank of the group. For the five-graviton scattering, on the other hand, we show that the amplitude vanishes whenever the process is planar, without imposing further kinematic conditions. A rationale for this result is provided using color-kinematics duality.
Tests of Chiral perturbation theory with COMPASS
Directory of Open Access Journals (Sweden)
Friedrich Jan M.
2014-06-01
Full Text Available The COMPASS experiment at CERN accesses pion-photon reactions via the Primakoff effect., where high-energetic pions react with the quasi-real photon field surrounding the target nuclei. When a single real photon is produced, pion Compton scattering is accessed and from the measured cross-section shape, the pion polarisability is determined. The COMPASS measurement is in contradiction to the earlier dedicated measurements, and rather in agreement with the theoretical expectation from ChPT. In the same experimental data taking, reactions with neutral and charged pions in the final state are measured and analyzed in the context of chiral perturbation theory.
Chiral Dynamics of Baryons from String Theory
Hong, D K; Yee, H U; Yi, P; Hong, Deog Ki; Rho, Mannque; Yee, Ho-Ung; Yi, Piljin
2007-01-01
We study baryons in an AdS/CFT model of QCD by Sakai and Sugimoto, realized as small instantons with fundamental string hairs. We introduce an effective field theory of the baryons in the five-dimensional setting, and show that the instanton interpretation implies a particular magnetic coupling. Dimensional reduction to four dimensions reproduces the usual chiral effective action, and in particular we estimate the axial coupling $g_A$ between baryons and pions and the magnetic dipole moments, both of which are proportional to $N_c$. We extrapolate to finite $N_c$ and discuss subleading corrections.
Scattering lengths in SU(2) gauge theory with two fundamental fermions
DEFF Research Database (Denmark)
Arthur, R.; Drach, V.; Hansen, Martin Rasmus Lundquist; Hietanen, A.; Pica, C.; Sannino, F.
2014-01-01
We investigate non perturbatively scattering properties of Goldstone Bosons in an SU(2) gauge theory with two Wilson fermions in the fundamental representation. Such a theory can be used to build extensions of the Standard Model that unifies Technicolor and pseudo Goldstone composite Higgs models...... particular the expected chiral symmetry breaking pattern. We then discuss how to compute them on the lattice and give preliminary results using finite size methods....
Monopoles and confinement in lattice gauge theory
International Nuclear Information System (INIS)
The mechanism by which quarks, believed to be the fundamental constituents of matter, are prevented from existing in the free state is fundamental problems in physics. One of the most viable candidates for a hypothesis of confinement is the dual superconductor mechanism that likens quark confinement to the Meissner effect in superconductors. The peculiarities of quark interactions make a numerical approach to the subject a necessity, and therefore, much of the work in this area has been done through the methods of lattice gauge theory, with the simplicities afforded by putting spacetime on a four-dimensional grid. Over the years a large amount of indirect evidence has accumulated that the dual superconductor hypothesis does indeed lead to quark confinement but unambiguous evidence has eluded research efforts until recently. This work presents the first direct proof of a Meissner-like effect that leads to confinement, using the numerical techniques of lattice gauge theory. It is shown that for a U(1) lattice gauge theory, that serves as a toy model of the real world of quarks, a dual London relation and an electric fluxoid qauntization condition is satisfied, allowing the author to conclude that the vacuum in this case acts like an extreme type-II superconductor, and that quarks are confined. The author also shows that SU(2) lattice gauge theory, which is qualitatively different and another step closer to reality, shows a Meissner-like effect. In contrast to the U(1) case, the author's results are found consistent with a dual version of the Ginsburg-Landau theory of superconductor on the borderline between type-I and type-II. This approach paves the wave for a study of the more complicated theory, quantum chromodynamics, that is believed to describe quarks
Strong dynamics and lattice gauge theory
Schaich, David
In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ≈ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses
Strings - Links between conformal field theory, gauge theory and gravity
International Nuclear Information System (INIS)
String theory is a candidate framework for unifying the gauge theories of interacting elementary particles with a quantum theory of gravity. The last years we have made considerable progress in understanding non-perturbative aspects of string theory, and in bringing string theory closer to experiment, via the search for the Standard Model within string theory, but also via phenomenological models inspired by the physics of strings. Despite these advances, many deep problems remain, amongst which a non-perturbative definition of string theory, a better understanding of holography, and the cosmological constant problem. My research has concentrated on various theoretical aspects of quantum theories of gravity, including holography, black holes physics and cosmology. In this Habilitation thesis I have laid bare many more links between conformal field theory, gauge theory and gravity. Most contributions were motivated by string theory, like the analysis of supersymmetry preserving states in compactified gauge theories and their relation to affine algebras, time-dependent aspects of the holographic map between quantum gravity in anti-de-Sitter space and conformal field theories in the bulk, the direct quantization of strings on black hole backgrounds, the embedding of the no-boundary proposal for a wave-function of the universe in string theory, a non-rational Verlinde formula and the construction of non-geometric solutions to supergravity
Quantum walks and discrete gauge theories
Arnault, Pablo; Debbasch, Fabrice
2016-05-01
A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E ×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.
Chiral perturbation theory for lattice QCD
International Nuclear Information System (INIS)
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Chiral perturbation theory for lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Baer, Oliver
2010-07-21
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed. (orig.)
Hadronic Lorentz Violation in Chiral Perturbation Theory
Kamand, Rasha; Schindler, Matthias R
2016-01-01
Any possible Lorentz violation in the hadron sector must be tied to Lorentz violation at the underlying quark level. The relationships between the theories at these two levels are studied using chiral perturbation theory. Starting from a two-flavor quark theory that includes dimension-four Lorentz-violation operators, the effective Lagrangians are derived for both pions and nucleons, with novel terms appearing in both sectors. Since the Lorentz violation coefficients for nucleons and pions are all related to a single set of underlying quark coefficients, it is possible to place approximate bounds on pion Lorentz violation using only proton and neutron observations. The resulting bounds on four pion parameters are at the $10^{-23}$ level, representing improvements of ten orders of magnitude.
Interpolating between MAG and no-gauge in SU(2) gauge theory
International Nuclear Information System (INIS)
We perform the exploratory study of the pure gauge SU(2) theory with the interpolating gauge which interpolates between Maximally Abelian gauge (MAG) and no-gauge cases. We show that there is no smooth transition with respect to the interpolating parameter λ
M-Theory and Maximally Supersymmetric Gauge Theories
Lambert, Neil
2012-01-01
In this informal review for non-specalists we discuss the construction of maximally supersymmetric gauge theories that arise on the worldvolumes branes in String Theory and M-Theory. Particular focus is made on the relatively recent construction of M2-brane worldvolume theories. In a formal sense, the existence of these quantum field theories can be viewed as predictions of M-Theory. Their construction is therefore a reinforcement of the ideas underlying String Theory and M-Theory. We also br...
Chiral and deconfinement phase transition in the Hamiltonian approach to QCD in Coulomb gauge
Reinhardt, H
2016-01-01
The chiral and deconfinement phase transitions are investigated within the variational Hamiltonian approach to QCD in Coulomb gauge. The temperature $\\beta^{-1}$ is introduced by compactifying a spatial dimension. Thereby the whole temperature dependence is encoded in the vacuum state on the spatial manifold $\\mathbb{R}^2 \\times S^1(\\beta)$. The chiral quark condensate and the dual quark condensate (dressed Polyakov loop) are calculated as function of the temperature. From their inflection points the pseudo-critical temperatures for the chiral and deconfinement crossover transitions are determined. Using the zero-temperature quark and gluon propagators obtained within the variational approach as input, we find 226 MeV and 262 MeV, respectively, for the chiral and deconfinement transition.
Present status of lattice gauge theories
International Nuclear Information System (INIS)
The lattice formulation of the quark-gluon theory of strong interactions is outlined. No matter a version of the lattice gauge theory the ''string bit'' representation is used to solve the problem of the strong coupling expansion. A brief discussion is given of some major problems arising for: (1) large coupling and large lattice spacing, (2) the crossover from the gluon representation at small distances to the string representation at large ones, (3) constructing the strong coupling ground state at each lattice site independently, and (4) formulating the free quark theory on the lattice
Local models of gauge mediated supersymmetry breaking in string theory
International Nuclear Information System (INIS)
We describe local Calabi-Yau geometries with two isolated singularities at which systems of D3- and D7-branes are located, leading to chiral sectors corresponding to a semi-realistic visible sector and a hidden sector with dynamical supersymmetry breaking. We provide explicit models with a 3-family MSSM-like visible sector, and a hidden sector breaking supersymmetry at a meta-stable minimum. For singularities separated by a distance smaller than the string scale, this construction leads to a simple realization of gauge mediated supersymmetry breaking in string theory. The models are simple enough to allow the explicit computation of the massive messenger sector, using dimer techniques for branes at singularities. The local character of the configurations makes manifest the UV insensitivity of the supersymmetry breaking mediation
Extended objects in a gauge theory
International Nuclear Information System (INIS)
The covariant description of extended objects (Soliton) in the quantum field theory of two dimensions using relativistically covariant collective coordinates was presented previously. This method can be applied to higher dimensions and gauge theories. In this paper, the Abelian Higgs model in three dimensions is discussed. The Lagrangian density with primary and secondary constraints is introduced. Some choice of the gauge conditions is made, and six numbers of coordinates are introduced. The variables are transformed by Poincare transformation. First, the constraints of the gauge field is solved by adding a secondary constraint. The other six constraints associated with collective coordinates are consistent with each other with respect to the Dirac bracket. The gauge conditions are fixed so that the new frame means a body fixed one. The calculation of the mass of an extended object can be done. Rotational collective spectra appear in a mass term from the integration of these zero-energy modes. Finally, a scalar form factor of the extended object in three dimensions is presented. (Kato, T.)
Homotopical Poisson reduction of gauge theories
Paugam, Frederic
2011-01-01
The classical Poisson reduction of a given Lagrangian system with (local) gauge symmetries has to be done before its quantization. We propose here a coordinate free and self-contained mathematical presentation of the covariant Batalin-Vilkovisky Poisson reduction of a general gauge theory. It was explained in physical terms (DeWitt indices) in Henneaux and Teitelboim's book on quantization of gauge theories. It was studied in coordinates using jet spaces by Barnich-Brandt-Henneaux and Stasheff, among others. The main idea of our approach is to use the functor of point approach to spaces of fields to gain coordinate free geometrical insights on the spaces in play, and to focus on the notion of Noether identities, that is a simple replacement of the notion of gauge symmetry, harder to handle algebraically. Our main results are a precise formulation and understanding of the optimal finiteness hypothesis necessary for the existence of a solution of the classical master equation, and an interpretation of the Batal...
Gravity, Gauge Theories and Geometric Algebra
Lasenby, A; Gull, S F; Lasenby, Anthony; Doran, Chris; Gull, Stephen
1998-01-01
A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure selects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These e...
Mathematical and physical aspects of gauge theories
International Nuclear Information System (INIS)
We present here a survey of gauge theories, trying to relate the main mathematical and physical concepts. Part I is devoted to exhibiting parallel transport and connection as the adequate concepts for the constitution of the parametrized internal space of a particle. A covariant derivative provides the differential calculus, which is needed when one leaves the point-like description in microphysics. Part II deals with the so-called pure gauge theory and sketches the construction of the self-dual solutions of Yang-Mills equations. We briefly explain Guersey's method to get SU2 self-dual potentials as quarternionic analytic maps from S4 (first quarternionic projective space) into HPsub(n) (n-dimensional quarternionic projective space). Part III is devoted to the Goldstone's theorem and Higgs' mechanism used to provide a mass to gauge mesons. We describe a Salam-Weinberg model to illustrate these techniques. Part IV deals with the perturbative aspect. The Faddeev-Popov method, formerly conceived as a technique to get correct Feynmann rules, actually leads to a systematic study of the affine space of connections factored out by gauge transformations. (orig.)
Chiral perturbation theory for nucleon generalized parton distributions
Energy Technology Data Exchange (ETDEWEB)
Diehl, M. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Manashov, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik]|[Sankt-Petersburg State Univ. (Russian Federation). Dept. of Theoretical Physics; Schaefer, A. [Regensburg Univ. (Germany). Inst. fuer Physik 1 - Theoretische Physik
2006-08-15
We analyze the moments of the isosinglet generalized parton distributions H, E, H, E of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. (orig.)
Low-Energy Constants from Resonance Chiral Theory
Pich, Antonio
2008-01-01
I discuss the recent attempts to build an effective chiral Lagrangian incorporating massive resonance states. A useful approximation scheme to organize the resonance Lagrangian is provided by the large-Nc limit of QCD. Integrating out the resonance fields, one recovers the usual chiral perturbation theory Lagrangian with explicit values for the low-energy constants, parameterized in terms of resonance masses and couplings. The resonance chiral theory generates Green functions that interpolate...
Nonperturbative solution of Yukawa theory and gauge theories
Hiller, J. R.
2004-01-01
Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang-Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to include two-boson contributions to the dressed fermion state and has inspired similar work on QED, where Feynman gauge has been found surprisingly convenient. In both cases, the theories are regulated in the ultraviolet by the inclusion of Pauli-Villars particl...
Lagrangian Formulations of Self-dual Gauge Theories in Diverse Dimensions
Chen, Wei-Ming
2010-01-01
In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral $n$-form gauge theories, for $n = 2p$ in $D = 4p+2$ dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG model, we generalize the earlier Lagrangian formulation based on a decomposition of spacetime into $(D-1)$ dimensions plus a special dimension, to construct Lagrangian formulations based on a generic decomposition of spacetime into $D'$ and $D" = D - D'$ dimensions. Although the Lorentz symmetry is not manifest, we prove that the action is invariant under modified Lorentz transformations.
New relations for gauge-theory amplitudes
International Nuclear Information System (INIS)
We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multiloop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye (KLT) relations between gauge and gravity tree amplitudes. This insight leads to similar but novel relations. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
New Relations for Gauge-Theory Amplitudes
Bern, Z; Johansson, H
2008-01-01
We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
Holographic Entanglement in a Noncommutative Gauge Theory
Fischler, Willy; Kundu, Sandipan
2014-01-01
In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties.
Generalized string theory mapping relations between gravity and gauge theory
Bjerrum-Bohr, N E J
2003-01-01
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, -- linking diagrams in gravity and Yang-Mills theory, -- as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings.
Generalized string theory mapping relations between gravity and gauge theory
International Nuclear Information System (INIS)
A previous study of the Kawai, Lewellen and Tye (KLT) relations between gravity and gauge theories, imposed by the relationship of closed and open strings, are here extended in the light of general relativity and Yang-Mills theory as effective field theories. We discuss the possibility of generalizing the traditional KLT mapping in this effective setting. A generalized mapping between the effective Lagrangians of gravity and Yang-Mills theory is presented, and the corresponding operator relations between gauge and gravity theories at the tree level are further explored. From this generalized mapping remarkable diagrammatic relations are found, linking diagrams in gravity and Yang-Mills theory, as well as diagrams in pure effective Yang-Mills theory. Also the possibility of a gravitational coupling to an antisymmetric field in the gravity scattering amplitude is considered, and shown to allow for mixed open-closed string solutions, i.e., closed heterotic strings
Tests and present status of gauge theories
International Nuclear Information System (INIS)
The author discusses the predictions of the standard model for strong, weak and electromagnetic interactions. The Abelian Model is presented to represent gauge theories at work. Hadronic structure functions are explained which describe the distribution of quarks and gluons within the initial state hadrons. Hadronic fragmentation functions are defined and illustrated. A set of exercises is presented which may be helpful toward understanding the material presented
Vortices in SU(2) lattice gauge theory
Cheluvaraja, S.
2000-01-01
We investigate some properties of thick vortices and thick monopoles in the SU(2) lattice gauge theory by inserting operators which create these excitations. Some quantities associated with the dynamical behaviour of thick vortices and thick monopoles are studied. We measure the derivative of the free energy of the vortex with respect to the coupling and we find that it falls exponentially with the cross sectional area of the vortex size. We also study the monopole-monopole potential energy f...
Gauge theories with non-trivial backgrounds
Binosi, Daniele
2014-01-01
We review our most recent results in formulating gauge theories in the presence of a background field on the basis of symmetry arguments only. In particular we show how one can gain full control over the dependence on the background field of the effective action, and how the so-called background field method emerges naturally from the requirement of invariance under the BRST and antiBRST symmetries.
Open+Closed String Field Theory From Gauge Fields
Gomis, Jaume; Moriyama, Sanefumi(Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan); Park, Jongwon
2003-01-01
We study open and closed string interactions in the Type IIB plane wave background using open+closed string field theory. We reproduce all string amplitudes from the dual N=2 Sp(N) gauge theory by computing matrix elements of the dilatation operator. A direct diagrammatic correspondence is found between string theory and gauge theory Feynman diagrams. The prefactor and Neumann matrices of open+closed string field theory are separately realized in terms of gauge theory quantities.
On the color simple group from chiral electroweak gauge groups
Doff, A.(Universidade Tecnológica Federal do Paraná – UTFPR – DAFIS, Av. Monteiro Lobato Km 04, 84016-210 Ponta Grossa, PR, Brazil); Pisano, F
2000-01-01
Following the pioneering Okubo scrutiny of gauge simple groups for the quantum chromodynamics we show the constraints coming from the wondrous predictive leptoquark-bilepton flavordynamics connecting the number of color charges to solution of the flavor question and to an electric charge quantization unconstrained from the Dirac, Majorana or Dirac--Majorana character of massive neutrino.
On the variational formulation of classical Abelian gauge field theories
International Nuclear Information System (INIS)
It is shown how one can formulate an action principle for classical Abelian gauge theories not by means of gauge potentials and currents but in terms of the gauge invariant field strengths and gauge variant stream potentias. The discussion is on a general formal level in n=s+t space-time dimensions and uses, for brevity, the language of differential forms
Nonequilibrium formulation of abelian gauge theories
International Nuclear Information System (INIS)
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at each perturbative
Nonequilibrium formulation of abelian gauge theories
Energy Technology Data Exchange (ETDEWEB)
Zoeller, Thorsten
2013-09-01
This work is about a formulation of abelian gauge theories out-of-equilibrium. In contrast to thermal equilibrium, systems out-of-equilibrium are not constant in time, and the interesting questions in such systems refer to time evolution problems. After a short introduction to quantum electrodynamics (QED), the two-particle irreducible (2PI) effective action is introduced as an essential technique for the study of quantum field theories out-of-equilibrium. The equations of motion (EOMs) for the propagators of the theory are then derived from it. It follows a discussion of the physical degrees of freedom (DOFs) of the theory, in particular with respect to the photons, since in covariant formulations of gauge theories unphysical DOFs are necessarily contained. After that the EOMs for the photon propagator are examined more closely. It turns out that they are structurally complicated, and a reformulation of the equations is presented which for the untruncated theory leads to an essential structural simplification of the EOMs. After providing the initial conditions which are necessary in order to solve the EOMs, the free photon EOMs are solved with the help of the reformulated equations. It turns out that the solutions diverge in time, i.e. they are secular. This is a manifestation of the fact that gauge theories contain unphysical DOFs. It is reasoned that these secularities exist only in the free case and are therefore ''artificial''. It is however emphasized that they may not be a problem in principle, but certainly are in practice, in particular for the numerical solution of the EOMs. Further, the origin of the secularities, for which there exists an illustrative explanation, is discussed in more detail. Another characteristic feature of 2PI formulations of gauge theories is the fact that quantities calculated from approximations of the 2PI effective action, which are gauge invariant in the exact theory as well as in an approximated theory at
1/N/sup 2/ expansion of the mean field for lattice chiral and gauge models
Energy Technology Data Exchange (ETDEWEB)
Brihaye, Y.; Taormina, A.
1985-08-21
For lattice chiral and gauge models the authors develop an /sup 1//N/sup 2/ expansion of the mean-field approximation. Special attention is paid to the free energy for which the effect of fluctuations around the mean-field solution is presented as an /sup 1//N/sup 2/ expansion. The differences between U(N) and SU(N) are pointed out. Finally, for the chiral model the mean-field saddle-point technique is applied to compute the two-point correlation function. (author).
Gauge Theory of Gravity and Supergravity
Kaul, Romesh K.
2006-01-01
We present a formulation of gravity in terms of a theory based on complex SU(2) gauge fields with a general coordinate invariant action functional quadratic in the field strength. Self-duality or anti-self-duality of the field strength emerges as a constraint from the equations of motion of this theory. This in turn leads to Einstein gravity equations for a dilaton and an axion conformally coupled to gravity for the self-dual constraint. The analysis has also been extended to N=1 and 2 super ...
Higher-dimensional gauge theories from string theory
Energy Technology Data Exchange (ETDEWEB)
Tomasiello, Alessandro [Dipartimento di Fisica, Universita di Milano-Bicocca, Milano (Italy); INFN, Sezione di Milano-Bicocca, Milano (Italy)
2016-04-15
We review some recent developments regarding supersymmetric field theories in six and five dimensions. In particular, we will describe the classification of supersymmetric six-dimensional theories with a holographic IIA dual; they are ''linear quivers'' consisting of chains of many SU (or SO/Sp) gauge groups connected by hypermultiplets and tensor multiplets. We will also describe the wider classification of supersymmetric six-dimensional theories that can be engineered in F-theory; these are also chains, but they include exceptional gauge groups and copies of a more exotic ''E-string'' theory with a single tensor and E{sub 8} flavor symmetry. Finally we discuss some properties of these theories under compactification to lower dimensions. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Spectrum of SU(2) lattice gauge theory with two adjoint Dirac flavours
International Nuclear Information System (INIS)
An SU(2) gauge theory with two fermions transforming under the adjoint representation of the gauge group may appear conformal or almost conformal in the infrared. We use lattice simulations to study the spectrum of this theory and present results on the masses of several gauge singlet states as a function of the physical quark mass determined through the axial Ward identity and find indications of a change from chiral symmetry breaking to a phase consistent with conformal behaviour at βL ∼ 2. However, the measurement of the spectrum is not alone sufficient to decisively confirm the existence of conformal fixed point in this theory as we show by comparing to similar measurements with fundamental fermions. Based on the results we sketch a possible phase diagram of this lattice theory and discuss the applicability and importance of these results for the future measurement of the evolution of the coupling constant.
Spinning black holes in a gauge theory of gravitation
BabeÅ£i (Pretorian), Simona
2013-11-01
Spinning black holes are presented in terms of gauge fields in a commutative gauge theory of gravitation. The field strength tensor comes as a consequence of the particular ansatz for gauge fields. In order to obtain spinning black holes in a noncommutative gauge theory of gravitation is used an analytical procedure conceived in GRTensorII. To calculate the leading noncommutative corrections and to choose an appropriate noncommutative parameter are used recursive relations. The gauge fields and the field strength tensor for a spinning mass preserves some features of other cosmological solutions in the gauge theory of gravitation and the noncommutative corrections are expected to provide some important physical insights.
Inflation and gauge mediation in supersymmetric gauge theory
International Nuclear Information System (INIS)
We propose a simple high-scale inflationary scenario based on a phenomenologically viable model with direct gauge mediation of low-scale supersymmetry breaking. Hybrid inflation occurs in a hidden supersymmetry breaking sector. Two hierarchical mass scales to reconcile both high-scale inflation and gauge mediation are necessary for the stability of the metastable supersymmetry breaking vacuum. Our scenario is also natural in light of the Landau pole problem of direct gauge mediation. (author)
Finite-temperature study of eight-flavor SU(3) gauge theory
Schaich, David; Rinaldi, Enrico
2015-01-01
We present new lattice investigations of finite-temperature transitions for SU(3) gauge theory with Nf=8 light flavors. Using nHYP-smeared staggered fermions we are able to explore renormalized couplings $g^2 \\lesssim 20$ on lattice volumes as large as $48^3 \\times 24$. Finite-temperature transitions at non-zero fermion mass do not persist in the chiral limit, instead running into a strongly coupled lattice phase as the mass decreases. That is, finite-temperature studies with this lattice action require even larger $N_T > 24$ to directly confirm spontaneous chiral symmetry breaking.
A complete gauge theory for the whole Poincare group
International Nuclear Information System (INIS)
Gauge theories for non-semisimple groups are examined. A theory for the Poincare group with all the essential characteristics of a Yang-Mills theory possesses necessarily extra equations. Inonu-Wigner contractions of gauge theories are introduced which provide a Lagrangian formalism, equivalent to a lagrangian de Sitter theory supplemented by weak constraints. (Author)
Double chiral logarithms of Generalized Chiral Perturbation Theory for low-energy pi-pi scattering
L. GirlandaPadua U. & INFN
2015-01-01
We express the two-massless-flavor Gell-Mann--Oakes--Renner ratio in terms of low-energy pi-pi observables, including the O(p^6) double chiral logarithms of generalized chiral perturbation theory. Their contribution is sizeable and tends to compensate the one from the single chiral logarithms. However it is not large enough to spoil the convergence of the chiral expansion. As a signal of reduced theoretical uncertainty, we find that the scale dependence from the one-loop single logarithms is ...
Flavour singlets in gauge theory as Permutations
Kimura, Yusuke; Suzuki, Ryo
2016-01-01
Gauge-invariant operators can be specified by equivalence classes of permutations. We develop this idea concretely for the singlets of the flavour group $SO(N_f)$ in $U(N_c)$ gauge theory by using Gelfand pairs and Schur-Weyl duality. The singlet operators, when specialised at $N_f =6$, belong to the scalar sector of ${\\cal N}=4$ SYM. A simple formula is given for the two-point functions in the free field limit of $g_{YM}^2 =0$. The free two-point functions are shown to be equal to the partition function on a 2-complex with boundaries and a defect, in a topological field theory of permutations. The permutation equivalence classes are Fourier transformed to a representation basis which is orthogonal for the two-point functions at finite $N_c , N_f$. Counting formulae for the gauge-invariant operators are described. The one-loop mixing matrix is derived as a linear operator on the permutation equivalence classes.
Monte Carlo calculations in lattice gauge theories
International Nuclear Information System (INIS)
This paper covers the following: a few words of motivation for numerical simulations, and a description of the Monte Carlo method as applied to lattice gauge theories. This is followed by a discussion of systems that contain bosonic degrees of freedom only. The authors review Monte Carlo results for pure gauge systems, illustrating the determination of a variety of observables - the string tension, the potential, the temperature at which quarks become deconfined, and attempts to calculate the mass gap of the theory, also called the glue-ball mass. They try to explain what happens if one considers various types of the action, how one verifies universality in the passage to the continuum limit and we mention briefly simulations applied to systems that go beyond just gauge fields and include other bosonic fields, known in general as Higgs scalars. Finally they consider fermions on the lattice, pointing out conceptual problems in the formulation of the Dirac equation on the lattice, and then discussing the difficulties that arise in attempting to apply the same kind of numerical methods to fermionic systems, the approximations and the techniques that are used to overcome these problems and some of the numerical results
Matrix product states for gauge field theories
Buyens, Boye; Van Acoleyen, Karel; Verschelde, Henri; Verstraete, Frank
2013-01-01
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour quantum electrodynamics, also known as the massive Schwinger model, and are able to determine very accurately the ground state properties and elementary one-particle excitations in the continuum limit. In particular, a novel particle excitation in the form of a heavy vector boson is uncovered, compatible with the strong coupling expansion in the continuum. We also study non-equilibrium dynamics by simulating the real-time evolution of the system induced by a quench in the form of a uniform background electric field.
UV caps and modulus stabilization for 6D gauged chiral supergravity
International Nuclear Information System (INIS)
We describe an explicit UV regularization of the brane singularities for all 4D flat configurations of 6D gauged chiral supergravity compactified on axially symmetric internal spaces (for which the general solutions are known). All such solutions have two or fewer co-dimension two singularities, which we resolve in terms of microscopic co-dimension one cylindrical 4-branes, whose interiors are capped using the most general possible 4D flat solution of the 6D field equations. By so doing we show that such a cap is always possible for any given bulk geometry, and obtain an explicit relationship between the properties of the capped 4-branes and the various parameters which describe the bulk solution. We show how these branes generically stabilize the size of the extra dimensions by breaking the scale invariance which relates classical solutions to 6D supergravity, and we compute the scalar potential for this modulus in the 4D effective theory. The lifting of this marginal direction provides a natural realization of the Goldberger-Wise stabilization mechanism in six dimensions
An Ultraviolet Chiral Theory of the Top for the Fundamental Composite (Goldstone) Higgs
Cacciapaglia, Giacomo
2015-01-01
We introduce a scalar-less anomaly free chiral gauge theory that serves as natural ultraviolet completion of models of fundamental composite (Goldstone) Higgs dynamics. The new theory is able to generate the top mass and furthermore features a built-in protection mechanism that naturally suppresses the bottom mass. At low energies the theory predicts new fractionally charged fermions, and a number of four-fermion operators that, besides being relevant for the generation of the top mass, also lead to an intriguing phenomenology for the new states predicted by the theory.
Supersymmetric gauge theories, quantization of Mflat, and conformal field theory
International Nuclear Information System (INIS)
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.
Wess-Zumino terms for reducible anomalous gauge theories
International Nuclear Information System (INIS)
Reducible off-shell anomalous gauge theories are studied in the framework of an extended Field-Antifield formalism by introducing new variables associated with the anomalous gauge degrees of freedom. The Wess-Zumino term for these theories is constructed and new gauge invariances appear. The quantum effects due to the extra variables are considered. (orig.)
Dimensional reduction of four-dimensional topologically massive gauge theory
Kumar, R.; Lahiri, Amitabha
2015-01-01
We study topologically massive (B \\wedge F) Abelian and non-Abelian gauge theories in four dimensions, and reduce them to three dimensions by assuming that the fields do not propagate in one of the spatial directions. For certain gauge choices the reduced theories are the Jackiw-Pi models of massive gauge fields.
Relativistic Chiral Theory of Nuclear Matter and QCD Constraints
Chanfray, G.; Ericson, M.
2009-01-01
Talk given by G. Chanfray at PANIC 08, Eilat (Israel), november 10-14, 2008 We present a relativistic chiral theory of nuclear matter which includes the effect of confinement. Nuclear binding is obtained with a chiral invariant scalar background field associated with the radial fluctuations of the chiral condensate Nuclear matter stability is ensured once the scalar response of the nucleon depending on the quark confinement mechanism is properly incorporated. All the parameters are fixed o...
Four-Fermion Limit of Gauge-Yukawa Theories
DEFF Research Database (Denmark)
Krog, Jens; Mojaza, Matin; Sannino, Francesco
2015-01-01
perturbative gauge-Yukawa theories can have a strongly coupled limit at high-energy, that can be mapped into a four-fermion theory. Interestingly, we are able to precisely carve out a region of the perturbative parameter space supporting such a composite limit. This has interesting implications on our current......We elucidate and extend the conditions that map gauge-Yukawa theories at low energies into time-honoured gauged four-fermion interactions at high energies. These compositeness conditions permit to investigate theories of composite dynamics through gauge-Yukawa theories. Here we investigate whether...... view on models of particle physics. As a template model we use an $SU(N_C)$ gauge theory with $N_F$ Dirac fermions transforming according to the fundamental representation of the gauge group. The fermions further interact with a gauge singlet complex $N_F\\times N_F$ Higgs that ceases to be a physical...
Non-renormalization theorems for non-perturbative effects in SUSY gauge theories
International Nuclear Information System (INIS)
Supersymmetric gauge theories with Higgs mechanism are considered. After all heavy fields are integrated out we are left with the instanton-induced effective action for light fields. It is demonstrated that the one-loop instanton result is not modified by higher order perturbative corrections. The peculiarity of the case considered is that the background scalar fields do not possess definite chirality, and the bosonic and fermionic modes are not degenerate for this reason. (orig.)
Analogue of the Witten effect in the Poincare gauge theory of gravity
International Nuclear Information System (INIS)
The gravitational contribution to the chiral anomaly is analysed in the framework of the Poincare gauge theory. It is shown that an additional CP-violating term 8*RR in the effective Lagrangian is equivalent to a shift in the mass of the Taub-NUT metric as felt by fermions. This analogue of the Witten effect is discussed in conjunction with the appearance of torsion in recently found exact solutions. (author)
Bonelli, Giulio; Sciarappa, Antonio; Tanzini, Alessandro; Vasko, Petr
2014-07-01
We show that the exact partition function of U( N) six-dimensional gauge theory with eight supercharges on ℂ2 × 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.
Effective Kinetic Theory for High Temperature Gauge Theories
Arnold, P; Yaffe, L G; Arnold, Peter; Moore, Guy D.; Yaffe, Laurence G.
2003-01-01
Quasiparticle dynamics in relativistic plasmas associated with hot, weakly-coupled gauge theories (such as QCD at asymptotically high temperature $T$) can be described by an effective kinetic theory, valid on sufficiently large time and distance scales. The appropriate Boltzmann equations depend on effective scattering rates for various types of collisions that can occur in the plasma. The resulting effective kinetic theory may be used to evaluate observables which are dominantly sensitive to the dynamics of typical ultrarelativistic excitations. This includes transport coefficients (viscosities and diffusion constants) and energy loss rates. We show how to formulate effective Boltzmann equations which will be adequate to compute such observables to leading order in the running coupling $g(T)$ of high-temperature gauge theories [and all orders in $1/\\log g(T)^{-1}$]. As previously proposed in the literature, a leading-order treatment requires including both $22$ particle scattering processes as well as effect...
Non-Abelian gauge theories on non-commutative spaces
International Nuclear Information System (INIS)
The construction of a non-abelian gauge theory on non-commutative spaces is based on enveloping algebra-valued gauge fields. The number of independent field components is reduced to the number of gauge fields in a usual gauge theory. This is done with the help of the Seiberg-Witten map. The dynamics is formulated with a Lagrangian where additional couplings appear. (orig.)
Double-beta decay in gauge theories
International Nuclear Information System (INIS)
The double-beta decay in gauge theories is considered. The review of the 76Ge, 82Se, 96Zr, 100Cd, 128Te, 130Te, 136Xe and 150Nd experimental nuclear targets is presented. The mechanism of the Majorana intermediate neutrino is considered. The R-parity of the violation of the contribution to the 0νββ decay is studied. The effective nucleon currents in dependence on the momentum are discussed. The extraction of the lepton number, violating the double-β decay parameters is presented
Screening in two-dimensional gauge theories
Korcyl, Piotr
2012-01-01
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED2 as a warm-up for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Exact results in discretized gauge theories
International Nuclear Information System (INIS)
We apply the localization technique to topologically twisted N=(2,2) supersymmetric gauge theory on a discretized Riemann surface (the generalized Sugino model). We exactly evaluate the partition function and the vacuum expectation value (vev) of a specific Q-closed operator. We show that both the partition function and the vev of the operator depend only on the Euler characteristic and the area of the discretized Riemann surface and are independent of the details of the discretization. This localization technique may not only simplify the numerical analysis of supersymmetric lattice models but also connect the well defined equivariant localization to the empirical supersymmetric localization
Continuum regularization of gauge theory with fermions
International Nuclear Information System (INIS)
The continuum regularization program is discussed in the case of d-dimensional gauge theory coupled to fermions in an arbitrary representation. Two physically equivalent formulations are given. First, a Grassmann formulation is presented, which is based on the two-noise Langevin equations of Sakita, Ishikawa and Alfaro and Gavela. Second, a non-Grassmann formulation is obtained by regularized integration of the matter fields within the regularized Grassmann system. Explicit perturbation expansions are studied in both formulations, and considerable simplification is found in the integrated non-Grassmann formalism
Lattice Gauge Field Theory and Prismatic Sets
DEFF Research Database (Denmark)
Akyar, Bedia; Dupont, Johan Louis
particular the latter we use to study lattice gauge theory in the sense of Phillips and Stone. Thus for a Lie group and a set of parallel transport functions defining the transition over faces of the simplices, we define a classifying map from the prismatic star to a prismatic version of the classifying......We study prismatic sets analogously to simplicial sets except that realization involves prisms, i.e., products of simplices rather than just simplices. Particular examples are the prismatic subdivision of a simplicial set and the prismatic star of . Both have the same homotopy type as and in...... space of . In turn this defines a -bundle over the prismatic star....
Screening in two-dimensional gauge theories
Energy Technology Data Exchange (ETDEWEB)
Korcyl, Piotr [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki; Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Koren, Mateusz [Uniwersytet Jagiellonski, Cracow (Poland). Inst. Fizyki
2012-12-15
We analyze the problem of screening in 1+1 dimensional gauge theories. Using QED{sub 2} as a warmup for the non-abelian models we show the mechanism of the string breaking, in particular the vanishing overlap of the Wilson loops to the broken-string ground state that has been conjectured in higher-dimensional analyses. We attempt to extend our analysis to non-integer charges in the quenched and unquenched cases, in pursuit of the numerical check of a renowned result for the string tension between arbitrarily-charged fermions in the massive Schwinger model.
Beta function in supersymmetric gauge theoris
International Nuclear Information System (INIS)
Within the background field formalism vacuum loops in supersymmetric gauge theories are discussed. A direct connection is revealed between the absence (or presence) of high order contributions and infrared regularization. A simple explanation is given why the instanton amplitude is exhausted by one loop whilst in the standard supergraph technique the effective action contains terms of all orders in the coupling constant. Exact relation between the Gell-Mann-Low function and anomalous dimensions of matter superfields stemming from the instanton calculus are presented
The confining N = 1 supersymmetric gauge theories: A review
Energy Technology Data Exchange (ETDEWEB)
Csaki, C. [Univ. of California, Berkeley, CA (United States). Dept. of Physics]|[Lawrence Berkeley National Lab., CA (United States). Physics Div.
1998-08-01
The authors give a classification and overview of the confining N = 1 supersymmetric gauge theories. For simplicity they consider only theories based on simple gauge groups and no tree-level superpotential. Classification of these theories can be done according to whether or not there is a superpotential generated for the confined degrees of freedom. The theories with the superpotential include s-confining theories and also theories where the gauge fields participate in the confining spectrum, while theories with no superpotential include theories with a quantum deformed moduli space and theories with an affine moduli space.
On a Gauge Invariant Quantum Formulation for Non-gauge Classical Theory
I.L. Buchbinder; Pershin, V. D.; Toder, G. B.
1996-01-01
We propose a method of constructing a gauge invariant canonical formulation for non-gauge classical theory which depends on a set of parameters. Requirement of closure for algebra of operators generating quantum gauge transformations leads to restrictions on parameters of the theory. This approach is then applied for illustration to bosonic string theory coupled to background tachyonic field. It is shown that within the proposed canonical formulation the known mass-shell condition for tachyon...
Zohar, Erez; Cirac, J. Ignacio; Reznik, Benni
2013-01-01
Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local ga...
Anselmi, Damiano
2015-05-01
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry, and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost numbers satisfy a variant of the Kluberg-Stern-Zuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale Λ associated with them is kept fixed, the theory is superrenormalizable and has the property that, once the gauge anomalies are canceled at one loop, they manifestly vanish from two loops onwards by simple power counting. When the Λ divergences are subtracted away and Λ is sent to infinity, the anomaly cancellation survives in a manifest form within the truncation and in a nonmanifest form outside. The standard model coupled to quantum gravity satisfies all the assumptions, so it is free of gauge anomalies to all orders.
Quantum Link Models: A Discrete Approach to Gauge Theories
Chandrasekharan, S; Wiese, U.-J.
1996-01-01
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as quantum spin models are related to ordinary classical spin systems. Here U(1) and SU(2) quantum link models are constructed explicitly. As Hamiltonian theories quantum link models are nonrelativistic gauge theories with potential applications in condensed ...
Differential Geometrical Formulation of Gauge Theory of Gravity
Wu, Ning; Xu, Zhan; Zhang, Da-Hua
2002-01-01
Differential geometric formulation of quantum gauge theory of gravity is studied in this paper. The quantum gauge theory of gravity which is proposed in the references hep-th/0109145 and hep-th/0112062 is formulated completely in the framework of traditional quantum field theory. In order to study the relationship between quantum gauge theory of gravity and traditional quantum gravity which is formulated in curved space, it is important to find the differential geometric formulation of quantu...
Fermion-boson metamorphosis in a chiral invariant theory
International Nuclear Information System (INIS)
A chiral invariant theory in two dimensions with massless fermions is examined in its Bose form. Dynamical generation of mass occurs via boson transmutation, which preserves the chiral symmetry of the massless theory and is independent of the number of fermions. Several new features of the fermion theory, such as hidden symmetry, duality and triality symmetries are discovered. Some interesting connections with other two-dimensional models are also presented. (orig.)
Vanishing chiral couplings in the large-Nc resonance theory
Portolés, Jorge; Rosell, Ignasi; Ruiz Femenía, Pedro
2007-01-01
The construction of a resonance theory involving hadrons requires implementing the information from higher scales into the couplings of the effective Lagrangian. We consider the large-Nc chiral resonance theory incorporating scalars and pseudoscalars, and we find that, by imposing LO short-distance constraints on form factors of QCD currents constructed within this theory, the chiral low-energy constants satisfy resonance saturation at NLO in the 1/Nc expansion.
The non chiral fusion rules in rational conformal field theories
Rida, A
1999-01-01
We introduce a general method to construct the non chiral fusion rules in rational conformal field theories. We are particularly interested by the models of the complementary series or like-D series which are solutions of modular invariant partition function. The form proposed of the non chiral fusion rules has a structure of Zn grading.
Chiral Boson Theory on the Light-Front
Srivastava, P P
1999-01-01
The {\\it front form} framework for describing the quantized theory of chiral boson is discussed. It avoids the conflict with the requirement of the principle of microcausality as is found in the conventional equal- time treatment. The discussion of the Floreanini-Jackiw model and its modified version for describing the chiral boson becomes very transparent on the light-front.
Chiral perturbation theory and U(3)L x U(3)R chiral theory of mesons
International Nuclear Information System (INIS)
In terms of the path integration theory, we examine U(3)L x U(3)R chiral theory of mesons (Li model) through integrating out fields of vector and axial-vector mesons. The corresponding effective Lagrangian for pseudoscalar mesons at order p4 have been obtained, and five quark-mass independent coupling constants Li(i = 1, 2, 3, 9, 10) in it have been calculated. It has been found that they are in good agreement with the values of χPT's at μ = mp. (author). 12 refs, 1 tab
New results in topological field theory and Abelian gauge theory
International Nuclear Information System (INIS)
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological invariants known as the Seiberg-Witten invariants. Much of the necessary background material is given, including a crash course in topological field theory, cohomology of manifolds, topological gauge theory and the rudiments of four manifold theory. My main hope is to wet the readers appetite, so that he or she will wish to read the original works and perhaps to enter this field. (author). 41 refs, 5 figs
Perturbative expansion in gauge theories on compact manifolds
Adams, D H
1996-01-01
A geometric formal method for perturbatively expanding functional integrals arising in quantum gauge theories is described when the spacetime is a compact riemannian manifold without boundary. This involves a refined version of the Faddeev-Popov procedure using a generalised Lorentz gauge-fixing condition with background gauge field chosen to be a general critical point for the action functional. The refinement takes into account the gauge-fixing ambiguities coming from gauge transformations which leave the critical point unchanged, resulting in the absence of infrared divergences when the critical point is isolated modulo gauge transformations. The procedure can be carried out using only the subgroup of gauge transformations which are topologically trivial, possibly avoiding the usual problems which arise due to gauge-fixing ambiguities. For Chern-Simons gauge theory the method enables the partition function to be perturbatively expanded for a number of simple spacetime manifolds such as S^3 and lens spaces,...
Gauge parameter dependence in gauge theories (revised: subsection 2.3)
Kraus, E; Sibold, K.
1994-01-01
Dependence on the gauge parameters is an important issue in gauge theories: physical quantities have to be independent. Extending BRS transformations by variation of the gauge parameter into a Grassmann variable one can control gauge parameter dependence algebraically. As application we discuss the anomaly coefficient in the Slavnov-Taylor identity, $S$-matrix elements, the vector two-point-function and the coefficients of renormalization group and Callan-Symanzik equation.
International Nuclear Information System (INIS)
Possibility of gauge independence of wave-function renormalization constants is studied on the basis of gauge-field theories with gauge covariance. By use of the expression for the double-pole type propagator D tilde sub( f)(x), exploited by Zwanziger, it is asserted that D tilde sub( f)(0) can be consistently taken zero. As a consequence, all renormalization constants become gauge independent, contrary to the conventional understanding. (author)
Aspects of Entanglement Entropy for Gauge Theories
Soni, Ronak M
2015-01-01
A definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended Hilbert space obtained by taking the tensor product of the Hilbert space of states on each link of the lattice. This extended Hilbert space admits a tensor product decomposition by definition and allows a density matrix and entanglement entropy for the set of links of interest to be defined. Here, we continue the study of this extended Hilbert space definition with particular emphasis on the case of Non-Abelian gauge theories. We extend the electric centre definition of Casini, Huerta and Rosabal to the Non-Abelian case and find that it differs in an important term. We also find that the entanglement entropy does not agree with the maximum number of Bell pairs that can be extracted by the processes of entanglement distillation or dilution, and give protocols which achieve the maximum bound. Finally, we compute the topological ...
Algebraic differential calculus for gauge theories
International Nuclear Information System (INIS)
The guiding idea in this paper is that, from the point of view of physics, functions and fields are more important than the (space time) manifold over which they are defined. The line pursued in these notes belongs to the general framework of ideas that replaces the space M by the ring of functions on it. Our essential observation, underlying this work, is that much of mathematical physics requires only a few differential operators (Lie derivative, d, δ) operating on modules of sections of suitable bundles. A connection (=gauge potential) can be described by a lift of vector fields from the base to the total space of a principal bundle. Much of the information can be encoded in the lift without reference to the bundle structures. In this manner, one arrives at an 'algebraic differential calculus' and its graded generalization that we are going to discuss. We are going to give an exposition of 'algebraic gauge theory' in both ungraded and graded versions. We show how to deal with the essential features of electromagnetism, Dirac, Kaluza-Klein and 't Hooft-Polyakov monopoles. We also show how to break the symmetry from SU(2) to U(1) without Higgs field. We briefly show how to deal with tests particles in external fields and with the Lagrangian formulation of field theories. (orig./HSI)
Semiclassical spinning strings and confining gauge theories
International Nuclear Information System (INIS)
We study multi-charged rotating string states on Type II B regular backgrounds dual to confining SU(N) gauge theories with (softly broken) N=1 supersymmetry, in the infra red regime. After exhibiting the classical energy/charge relations for the folded and circular two-charge strings, we compute in the latter case the one loop sigma-model quantum correction. The classical relation has an expansion in positive powers of the analogous of the BMN effective coupling, while the quantum corrections are non perturbative in nature and are not subleading in the limit of infinite charge. We comment about the dual field theory multi-charged hadrons and the implications of our computation for the AdS/N=4 duality. (author)
Isomonodromic deformations and supersymmetric gauge theories
Takasaki, K; Takasaki, Kanehisa; Nakatsu, Toshio
1996-01-01
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isomonodromy problem), too, can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of N=2 SU(s) supersymmetric Yang-Mills theory without matter is considered in detail for illustration. The isomonodromy problem in this case is closely related to the third Painlev\\'e equation and its multicomponent analogues. An implicit relation to t\\tbar fusion of topological sigma models is thereby expected.
The Origins of Lattice Gauge Theory
International Nuclear Information System (INIS)
The main focus of this talk is an anecdotal account of the history underlying my 1974 article entitled 'Confinement of Quarks.' In preparing this talk, I will draw on a historical interview conducted by the project for History of Recent Science and Technology at the Dibner Institute for the History of Science and Technology at MIT, and on a theory of invention proposed by Peter Drucker in his book 'Innovation and Entrepreneurship.' I will explain this theory; no background is needed. The account will start with related work in the 1960's. I will end the talk with a plea for lattice gauge researchers to be alert for unexpected scalar or vector colored particles that are invisible to experimentalists yet could start to spoil the agreement of computations with experiment. Note: In association with the Symposium ' 'Lattice 2004,' June 21 to June 26, 2004.
Hadron QCD (Bound states in gauge theories)
International Nuclear Information System (INIS)
The general principles of the description of bound states in QED and QCD are proposed for the aim of construction of the consistent scheme of calculating hadron spectrum and interaction amplitudes. Such principles are the explicit solution of the Gauss equation for time component, the quantization of the minimal set physical variables and the choice of the time-axis of quantization in accordance with the Markov-Yukawa relativistic theory of bilocal fields. QCD constructed by these principles contains new infrared divergences, changing the behaviour of the Coulomb field on large distances. This divergences (like ones in QED) are removed out with the help of phenomenology, in this case, by taking into account the rising potential as the 'nonperturbative background' for a new perturbation theory. It is shown how in such hadron theory the parton model, nonrelativistic potential spectroscopy, chiral Lagrangian and confinement appear. The Dirac quantization method, renormalization group equations and lattice calculations in their conventional formulation are proved to be untenable for the description of bound states. 23 refs
Zohar, Erez; Reznik, Benni
2013-01-01
Quantum simulations of High Energy Physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge and Lorentz invariance. In this paper we discuss these special requirements, and present a new method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows to include local gauge invariance as a \\emph{fundamental} symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: compact QED (U(1)), SU(N) and Z_N, which can be used to build quantum simulators in 1+1 dimensions. We also present a new loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simul...
pi K scattering in effective chiral theory of mesons
Li, Bing An; Gao, Dao-Neng; Yan, Mu-Lin
1998-01-01
In the framework of an effective chiral theory of mesons, pi K scattering is stydied. The scattering lengths, phase shifts, and cross sections are calculated. Theoretical results agree well with data. There is no new parameter in this study.
Nuclear forces from chiral effective field theory: a primer
Epelbaum, Evgeny
2010-01-01
This paper is a write-up of introductory lectures on the modern approach to the nuclear force problem based on chiral effective field theory given at the 2009 Joliot-Curie School, Lacanau, France, 27 September - 3 October 2009.
Coupled Cluster Methods in Lattice Gauge Theory
Watson, Nicholas Jay
Available from UMI in association with The British Library. Requires signed TDF. The many body coupled cluster method is applied to Hamiltonian pure lattice gauge theories. The vacuum wavefunction is written as the exponential of a single sum over the lattice of clusters of gauge invariant operators at fixed relative orientation and separation, generating excitations of the bare vacuum. The basic approximation scheme involves a truncation according to geometrical size on the lattice of the clusters in the wavefunction. For a wavefunction including clusters up to a given size, all larger clusters generated in the Schrodinger equation are discarded. The general formalism is first given, including that for excited states. Two possible procedures for discarding clusters are considered. The first involves discarding clusters describing excitations of the bare vacuum which are larger than those in the given wavefunction. The second involves rearranging the clusters so that they describe fluctuations of the gauge invariant excitations about their self-consistently calculated expectation values, and then discarding fluctuations larger then those in the given wavefunction. The coupled cluster method is applied to the Z_2 and Su(2) models in 2 + 1D. For the Z_2 model, the first procedure gives poor results, while the second gives wavefunctions which explicitly display a phase transition with critical couplings in good agreement with those obtained by other methods. For the SU(2) model, the first procedure also gives poor results, while the second gives vacuum wavefunctions valid at all couplings. The general properties of the wavefunctions at weak coupling are discussed. Approximations with clusters spanning up to four plaquettes are considered. Excited states are calculated, yielding mass gaps with fair scaling properties. Insight is obtained into the form of the wavefunctions at all couplings.
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.
The Structure of Multiloop Amplitudes in Gauge and Gravity Theories
Bern, Z; Johansson, H
2010-01-01
We review the recently discovered duality between color and kinematics in gauge theories. This duality leads to a remarkably simple double-copy relation between diagrammatic numerators of gravity scattering amplitudes and gauge-theory ones. We summarize nontrivial evidence that the duality and double-copy property holds to all loop orders. We also comment on other developments, including a proof that the gauge-theory duality leads to the gravity double-copy property, and the identification of gauge-theory Lagrangians whose double copies yield gravity Lagrangians.
He, Huan; von Keyserlingk, Curt
2016-01-01
Dijkgraaf-Witten (DW) theories are of recent interest to the condensed matter community, in part because they represent topological phases of matter, but also because they characterize the response theory of certain symmetry protected topological (SPT) phases. However, as yet there has not been a comprehensive treatment of the spectra of these models in the field theoretic setting -- the goal of this work is to fill the gap in the literature, at least for a selection of DW models with abelian gauge groups but non-abelian topological order. As applications, various correlation functions and fusion rules of line operators are calculated. We discuss for example the appearance of non-abelian statistics in DW theories with abelian gauge groups.
A Manifestly Gauge-Invariant Approach to Quantum Theories of Gauge Fields
Ashtekar, A.; J. Lewandowski; Marolf, D.; Mourao, J; Thiemann, T.
2016-01-01
In gauge theories, physical histories are represented by space-time connections modulo gauge transformations. The space of histories is thus intrinsically non-linear. The standard framework of constructive quantum field theory has to be extended to face these {\\it kinematical} non-linearities squarely. We first present a pedagogical account of this problem and then suggest an avenue for its resolution.
From lattice gauge theories to hydrogen atoms
Directory of Open Access Journals (Sweden)
Manu Mathur
2015-10-01
Full Text Available We construct canonical transformations to obtain a complete and most economical realization of the physical Hilbert space Hp of pure SU(22+1 lattice gauge theory in terms of Wigner coupled Hilbert spaces of hydrogen atoms. One hydrogen atom is assigned to every plaquette of the lattice. A complete orthonormal description of the Wilson loop basis in Hp is obtained by all possible angular momentum Wigner couplings of hydrogen atom energy eigenstates |n l m〉 describing electric fluxes on the loops. The SU(2 gauge invariance implies that the total angular momenta of all hydrogen atoms vanish. The canonical transformations also enable us to rewrite the Kogut–Susskind Hamiltonian in terms of fundamental Wilson loop operators and their conjugate electric fields. The resulting loop Hamiltonian has a global SU(2 invariance and a simple weak coupling (g2→0 continuum limit. The canonical transformations leading to the loop Hamiltonian are valid for any SU(N. The ideas and techniques can also be extended to higher dimension.
The Hawking effect in abelian gauge theories
International Nuclear Information System (INIS)
In an effort to compare and contrast gravity with other field theories an investigation is made into whether the Hawking effect is a peculiarly gravitational phenomenon. It is found that the effect exists for a particular background abelian gauge field configuration, as well as certain background gravitational field configurations. Specifically, pair production in a uniform electric field is shown to admit a thermal interpretation. In an effort to find out just what is singular about gravity it is found that the Hawking temperature characteristic of a particular gravitational field configuration is independent of the properties of the quantum fields propagating theorem, in direct contrast to the gauge field case. This implies that if the one loop approximation is to be valid the electric field must be ''cold'' relative to the energy scales set by the quantum fields. In gravity, however, because of the existence of a fundamental scale, the Planck length, the gravitational field can be ''hot'' or ''cold'' and a one loop approximation still remain valid. copyright 1989 Academic Press, Inc
Invariant structures and static forces in gauge theories
International Nuclear Information System (INIS)
The problem of finding all gauge invariants is considered in connection with confinement. It is shown that any gauge invariant may be built of the exponential line integrals (strings) and local gauge group tensors. The Coulomb field structure is analyzed from this point of view. In the pure SU(n) gauge theory (no matter), a potential of interacting static sources is found to be linearly rising with distance. 16 refs.; 1 fig
Directory of Open Access Journals (Sweden)
Héctor Torres-Silva
2008-11-01
Full Text Available This paper introduces a physical chiral asymmetrical regauging to increase the coefficient of performance of an electric motor. A review of gauge theory and a consideration of the disposal of the Lorentz condition to achieve the chiral regauging are presented. The coefficient of performance terminology is introduced. A magnetic motor is discussed under a chiral approach which gives a Beltrami process.Este trabajo introduce un recalibre físico quiral asimétrico usado para aumentar el coficiente de rendimiento de un motor eléctrico. Se presenta una revisión de la teoría de calibres y se examina el descarte de la condición de Lorentz para obtener el recalibrado quiral. Se introduce el coeficiente de rendimiento y se analiza un motor magnético bajo el enfoque quiral que permite un proceso Beltrami.
Early history of gauge theories and weak interactions
International Nuclear Information System (INIS)
The paper deals with Weyl's attempt to unify gravitation and electromagnetism, Weyl's 1929 classic 'Electron and gravitation', Yang-Mills theory, parity violation and 2-component neutrino, chiral invariance and universal V-A interaction. 3 figs., 38 refs
Integrable Models, SUSY Gauge Theories, and String Theory
Nam, S
1996-01-01
We consider the close relation between duality in N=2 SUSY gauge theories and integrable models. Vario us integrable models ranging from Toda lattices, Calogero models, spinning tops, and spin chains are re lated to the quantum moduli space of vacua of N=2 SUSY gauge theories. In particular, SU(3) gauge t heories with two flavors of massless quarks in the fundamental representation can be related to the spec tral curve of the Goryachev-Chaplygin top, which is a Nahm's equation in disguise. This can be generaliz ed to the cases with massive quarks, and N_f = 0,1,2, where a system with seven dimensional phas e space has the relevant hyperelliptic curve appear in the Painlevé test. To understand the stringy o rigin of the integrability of these theories we obtain exact nonperturbative point particle limit of ty pe II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of SU(2) QCD w ith N_f =1 hypermultiplet.
Holographic repulsion and confinement in gauge theory
International Nuclear Information System (INIS)
We show that for asymptotically anti-de Sitter (AdS) backgrounds with negative energy, such as the AdS soliton and regulated negative-mass AdS–Schwarzshild metrics, the Wilson loop expectation value in the AdS/CFT conjecture exhibits a Coulomb to confinement transition. We also show that the quark–antiquark (q q-bar ) potential can be interpreted as affine time along null geodesics on the minimal string worldsheet and that its intrinsic curvature provides a signature of transition to confinement phase. Our results suggest a generic (holographic) relationship between confinement in gauge theory and repulsive gravity, which in turn is connected with singularity avoidance in quantum gravity. Communicated by P R L V Moniz (fast track communication)
Dimensionally continued multi-loop gauge theory
Broadhurst, D J
1999-01-01
A dimensionally continued background-field method makes the rationality of the 4-loop quenched QED beta function far more reasonable than had previously appeared. After 33 years of quest, dating from Rosner's discovery of 3-loop rationality, one finally sees cancellation of zeta values by the trace structure of individual diagrams. At 4-loops, diagram-by-diagram cancellation of $\\zeta(5)$ does not even rely on the values of integrals at d=4. Rather, it is a property of the rational functions of $d$ that multiply elements of the full d-dimensional basis. We prove a lemma: the basis consists of slices of wheels. We explain the previously mysterious suppression of $\\pi^4$ in massless gauge theory. The 4-loop QED result $\\beta_4=-46$ is obtained by setting d=4 in a precisely defined rational polynomial of d, with degree 11. The other 5 rational functions vanish at d=4.
A Mathematical Theory of the Gauged Linear Sigma Model
Fan, Huijun; Ruan, Yongbin
2015-01-01
We construct a rigorous mathematical theory of Witten's Gauged Linear Sigma Model (GLSM). Our theory applies to a wide range of examples, including many cases with non-Abelian gauge group. Both the Gromov-Witten theory of a Calabi-Yau complete intersection X and the Landau-Ginzburg dual (FJRW-theory) of X can be expressed as gauged linear sigma models. Furthermore, the Landau-Ginzburg/Calabi-Yau correspondence can be interpreted as a variation of the moment map or a deformation of GIT in the GLSM. This paper focuses primarily on the algebraic theory, while a companion article will treat the analytic theory.
Zohar, Erez; Cirac, J. Ignacio; Reznik, Benni
2013-08-01
Quantum simulations of high-energy physics, and especially of gauge theories, is an emerging and exciting direction in quantum simulations. However, simulations of such theories, compared to simulations of condensed matter physics, must satisfy extra restrictions, such as local gauge invariance and relativistic structure. In this paper we discuss these special requirements, and present a method for quantum simulation of lattice gauge theories using ultracold atoms. This method allows us to include local gauge invariance as a fundamental symmetry of the atomic Hamiltonian, arising from natural atomic interactions and conservation laws (and not as a property of a low-energy sector). This allows us to implement elementary gauge invariant interactions for three lattice gauge theories: U(1) (compact QED), ZN and SU(N) (Yang-Mills), which can be used to build quantum simulators in 1+1 dimensions. We also present a loop method, which uses the elementary interactions as building blocks in the effective construction of quantum simulations for d+1 dimensional lattice gauge theories (d>1), but unlike in previous proposals, here gauge invariance and Gauss's law are natural symmetries, which do not have to be imposed as a constraint. We discuss in detail the quantum simulation of 2+1 dimensional compact QED and provide a numerical proof of principle. The simplicity of the already gauge-invariant elementary interactions of this model suggests it may be useful for future experimental realizations.
What can supersymmetric gauge theories and string theory learn from each other?
International Nuclear Information System (INIS)
We selectively review the exact methods of Seiberg and Witten for solving supersymmetric gauge theories, and some extensions of their work. We discuss applications to nonabelian dualities of N=2 and N=1 gauge theories. We describe string and M-theory realizations of these gauge theories, and their use in deriving nonabelian dualities. (Author). 51 refs
S-Duality, Noncritical Open String and Noncommutative Gauge Theory
Rey, Soo-Jong; von Unge, Rikard
2000-01-01
We examine several aspects of S-duality of four-dimensional noncommutative gauge theory. By making duality transformation explicit, we find that S-dual of noncommutative gauge theory is defined in terms of dual noncommutative deformation. In `magnetic' noncommutative U(1) gauge theory, we show that, in addition to gauge bosons, open D-strings constitute important low-energy excitations: noncritical open D-strings. Upon S-duality, they are mapped to noncritical open F-strings. We propose that,...
From topological quantum field theories to supersymmetric gauge theories
International Nuclear Information System (INIS)
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 β 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)
On the definition of entanglement entropy in lattice gauge theories
Aoki, Sinya; Iritani, Takumi; Nozaki, Masahiro; Numasawa, Tokiro; Shiba, Noburo; Tasaki, Hal
2015-01-01
We focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an extended Hilbert space which contains gauge non-invariant states as well. Working in the extended Hilbert space, we can define entanglement entropy associated with an arbitrary subset of links, not only for abelian but also for non-abelian theories. We then derive the associated replica formula. We also discuss t...
Properties of the non-Gaussian fixed point in 4D compact U(1) lattice gauge theory
International Nuclear Information System (INIS)
We examine selected properties of the gauge-ball spectrum and fermionic variables in the vicinity of the recently discussed non-Gaussian fixed point of 4D compact U(1) lattice gauge theory within the quenched approximation. Approaching the critical point from within the confinement phase, our data support scaling of T1+- gauge-ball states in units of the string tension square root. The analysis of the chiral condensate within the framework of a scaling form for the equation of state suggests non mean-field values for the magnetic exponents δ and βexp. (orig.)
Finite Gauge Transformations and Geometry in Extended Field Theory
Chaemjumrus, N
2015-01-01
The recently derived expressions for finite gauge transformations in double field theory with duality group O(d,d) are generalised to give expressions for finite gauge transformations for extended field theories with duality group SL(5,R), SO(5,5) and E6. The generalised metrics are discussed.
Gauge transformations in Dirac theory of constrained systems
International Nuclear Information System (INIS)
An analysis of some aspects of gauge transformations in the context of Dirac's theory of constrained systems is made. A generator for gauge transformations is constructed by comparing phase space trajectories with the same initial data but different choices of the arbitrary functions. An application to the Yang-Mills theory is performed. (L.C.)
A Map between q-deformed and ordinary Gauge Theories
Mesref, L.
2002-01-01
In complete analogy with Seiberg-Witten map defined in noncommutative geometry we introduce a new map between a q-deformed gauge theory and an ordinary gauge theory. The construction of this map is elaborated in order to fit the Hopf algebra structure.
Pure Gauge theory in crystal lattice and Coulomb gases
International Nuclear Information System (INIS)
A method for the construction of classical gases, starting from a pure gauge theory, is described. The method is applied to the U(1) gauge theory in two spatial dimensions. For this model it's seen the vaccua appearing as a consequence of the quantization ambiguity. The connection between the vaccua and the confinement is discussed. (Author)
General Form of Dilaton Gravity and Nonlinear Gauge Theory
Ikeda, Noriaki; -I, Izawa K.
1993-01-01
We construct a gauge theory based on general nonlinear Lie algebras. The generic form of `dilaton' gravity is derived from nonlinear Poincar{\\' e} algebra, which exhibits a gauge-theoretical origin of the non-geometric scalar field in two-dimensional gravitation theory.
2d Affine XY-Spin Model/4d Gauge Theory Duality and Deconfinement
Energy Technology Data Exchange (ETDEWEB)
Anber, Mohamed M.; Poppitz, Erich; /Toronto U.; Unsal, Mithat; /SLAC /Stanford U., Phys. Dept. /San Francisco State U.
2012-08-16
We introduce a duality between two-dimensional XY-spin models with symmetry-breaking perturbations and certain four-dimensional SU(2) and SU(2) = Z{sub 2} gauge theories, compactified on a small spatial circle R{sup 1,2} x S{sup 1}, and considered at temperatures near the deconfinement transition. In a Euclidean set up, the theory is defined on R{sup 2} x T{sup 2}. Similarly, thermal gauge theories of higher rank are dual to new families of 'affine' XY-spin models with perturbations. For rank two, these are related to models used to describe the melting of a 2d crystal with a triangular lattice. The connection is made through a multi-component electric-magnetic Coulomb gas representation for both systems. Perturbations in the spin system map to topological defects in the gauge theory, such as monopole-instantons or magnetic bions, and the vortices in the spin system map to the electrically charged W-bosons in field theory (or vice versa, depending on the duality frame). The duality permits one to use the two-dimensional technology of spin systems to study the thermal deconfinement and discrete chiral transitions in four-dimensional SU(N{sub c}) gauge theories with n{sub f} {ge} 1 adjoint Weyl fermions.
Quark Confinement in Restricted SU(2) Gauge Theory
Deldar, Sedigheh; Mohamadnejad, Ahmad
2012-01-01
We apply Zwanziger formalism to Cho restricted $ SU(2) $ theory to obtain the potential in a static quark-antiquark pair. Cho restricted theory is a self-consistent subset of a non-Abelian $ SU(2) $ gauge theory which tries to describe the infrared regime of Yang-Mills gauge theories. In Zwanziger formalism, a local Lagrangian depending on two electric and magnetic gauge fields is constructed for the theories where both electric and magnetic charges exist. Based on this local Lagrangian the p...
SDiff Gauge Theory and the M2 Condensate
Bandos, Igor A
2009-01-01
We develop a general formalism for the construction of (supersymmetric) gauge theories of volume-preserving diffeomorphisms (SDiff), focusing on the D=3 superconformal SDiff(3) invariant `BLG' theory describing a condensate of M2-branes.
Differential formalism aspects of the gauge classical theories
International Nuclear Information System (INIS)
The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.)
Adler-bell-jackiw anomaly in lattice gauge theory
International Nuclear Information System (INIS)
The axial anomaly in lattice gauge theory with Wilson fermion is discussed. Under weak coupling approximation, we calculate the anomaly term systematically by path integral method. The result agrees with that obtained in continuum theory
Adler-Bell-Jackiw anomaly in lattice gauge theory
International Nuclear Information System (INIS)
The axial anomaly in lattice gauge theory with Wilson fermion is discussed. Under the weak coupling approximation, we calculate the anomaly term systematically by the path-integral method. The result agrees with that obtained in continuum theory
Numerical study of chiral plasma instability within the classical statistical field theory approach
Buividovich, P. V.; Ulybyshev, M. V.
2016-07-01
We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and noncompact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, the electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of the electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon, which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields that is not accompanied by the axial charge decay. This suggests that the relation between the inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.
Gravitation, gauge theories and differential geometry
International Nuclear Information System (INIS)
The purpose of this article is to outline various mathematical ideas, methods, and results, primarily from differential geometry and topology, and to show where they can be applied to Yang-Mills gauge theories and Einstein's theory of gravitation.We have several goals in mind. The first is to convey to physicists the bases for many mathematical concepts by using intuitive arguments while avoiding the detailed formality of most textbooks. Although a variety of mathematical theorems will be stated, we will generally give simple examples motivating the results instead of presenting abstract proofs. Another goal is to list a wide variety of mathematical terminology and results in a format which allows easy reference. The reader then has the option of supplementing the descriptions given here by consulting standard mathematical references and articles such as those listed in the bibliography. Finally, we intend this article to serve the dual purpose of acquainting mathematicians with some basic physical concepts which have mathematical ramifications; physical problems have often stimuladed new directions in mathematical thought. (orig./WL)
Finsler geometry, relativity and gauge theories
International Nuclear Information System (INIS)
This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)
Frobenius-Chern-Simons gauge theory
Bonezzi, Roberto; Sezgin, Ergin; Sundell, Per
2016-01-01
Given a set of differential forms on an odd-dimensional noncommutative manifold valued in an internal associative algebra H, we show that the most general cubic covariant Hamiltonian action, without mass terms, is controlled by an Z_2-graded associative algebra F with a graded symmetric nondegenerate bilinear form. The resulting class of models provide a natural generalization of the Frobenius-Chern-Simons model (FCS) that was proposed in arXiv:1505.04957 as an off-shell formulation of the minimal bosonic four-dimensional higher spin gravity theory. If F is unital and the Z_2-grading is induced from a Klein operator that is outer to a proper Frobenius subalgebra, then the action can be written on a form akin to topological open string field theory in terms of a superconnection valued in the direct product of H and F. We give a new model of this type based on a twisting of C[Z_2 x Z_4], which leads to self-dual complexified gauge fields on AdS_4. If F is 3-graded, the FCS model can be truncated consistently as...
Gauge field theories. I : Gauge fields, Goldstone theorem and Higgs phenomena
International Nuclear Information System (INIS)
This lecture on gauge field theories is presented in six sections. In Section I, some general features of the gauge field theories are considered. The simple example of electrodynamics is studied in detail. The minimal electromagnetic interaction; one parameter gauge theory, the non-Abelian gauge groups; Yang-Mills fields and the Universality of gauge field couplings are discussed. In Section II, the various problems that arise in the dynamics of Yang-Mills fields at classical and quantum level are discussed. Included in the discussion are : Field equations and identities, Canonical formalism, Quantization, and Mass of the gauge field quanta. In Section III, spontaneous symmetry breaking is discussed in the context of field theory. Goldstone theorom is clearly stated, proved and illustrated by simple examples. Goldstone quanta are explained. In Section IV, the Higg's phenomenon concerning Goldstone bosons and massless particles is studied in detail in the Abelian and non-Abelian Gauge formalisms. The working of the Higgs-Kibble mechanism is illustrated with examples. In Section V, the Weinberg-Salam model on the unification of weak and electromagnetic interactions of leptons, based on Higgs-Kibble mechanism is discussed in relation to electron type leptons. In the last Section VI, some aspects of spontaneously broken gauge theories connected with renormalizability are discussed. These include (a) high energy behaviour of tree graphs, (b) self-masses, (c) the anomaly problem, and (d) the safe algebra. (A.K.)
Nonperturbative Formulas for Central Functions of Supersymmetric Gauge Theories
Anselmi, D.; Freedman, D. Z.; Grisaru, M. T.; Johansen, A. A.
1997-01-01
For quantum field theories that flow between ultraviolet and infrared fixed points, central functions, defined from two-point correlators of the stress tensor and conserved currents, interpolate between central charges of the UV and IR critical theories. We develop techniques that allow one to calculate the flows of the central charges and that of the Euler trace anomaly coefficient in a general N=1 supersymmetric gauge theory. Exact, explicit formulas for $SU(N_c)$ gauge theories in the conf...
Renormalisation of gauge theories on general anisotropic lattices and high-energy scattering in QCD
Giordano, Matteo
2015-01-01
We study the renormalisation of $SU(N_c)$ gauge theories on general anisotropic lattices, to one-loop order in perturbation theory, employing the background field method. The results are then applied in the context of two different approaches to hadronic high-energy scattering. In the context of the Euclidean nonperturbative approach to soft high-energy scattering based on Wilson loops, we refine the nonperturbative justification of the analytic continuation relations of the relevant Wilson-loop correlators, required to obtain physical results. In the context of longitudinally-rescaled actions, we study the consequences of one-loop corrections on the relation between the $SU(N_c)$ gauge theory and its effective description in terms of two-dimensional principal chiral models.
Bosonic Part of 4d N=1 Supersymmetric Gauge Theory with General Couplings: Local Existence
Akbar, Fiki T; Triyanta,; Zen, Freddy P
2013-01-01
In this paper, we prove the local existence of the bosonic part of N=1 supersymmetric gauge theory in four dimensions with general couplings. We start with the Lagrangian of generally coupled vector and chiral multiplets with scalar potential turned on. Then, for the sake of simplicity, we set all fermions vanish at the level of equations of motions, so we only have the bosonic parts of the theory. We apply Segal's general theory to show the local existence of solutions of field equations of motions by taking K\\"ahler potential to be bounded above by U(n) symmetric K\\"ahler potential and the first derivative of gauge couplings to be at most linear growth functions.
Gauge theory of the normal state of high Tc superconductors
International Nuclear Information System (INIS)
Starting with the one band t - J model and using the slave boson method to enforce the constraint of no double occupations, we examine fluctuations about the uniform RVB mean field solution. We restrict our attention to a temperature region where the bosons are not bose condensed. The important low energy fluctuations are described by gauge fields which are related to fluctuations in the spin chirality. The Fermions and Bosons are strongly coupled to the gauge field, leading to a transport time or order h/2π/kBT in agreement with experiment. The model also exhibits a Fermi surface with area 1 - x where x is the doping concentration, consistent with Luttinger Theorem, but the low lying excitations have a decay width much larger than its energy, in violation of Landau's criterion for a Fermi liquid state. Other experimental implications of this model and the possibility of a direct measurement of the chirality fluctuations are discussed. (author). 69 refs, 11 figs
Quantum Monte Carlo calculations with chiral effective field theory interactions
International Nuclear Information System (INIS)
The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By
Quantum Monte Carlo calculations with chiral effective field theory interactions
Energy Technology Data Exchange (ETDEWEB)
Tews, Ingo
2015-10-12
The neutron-matter equation of state connects several physical systems over a wide density range, from cold atomic gases in the unitary limit at low densities, to neutron-rich nuclei at intermediate densities, up to neutron stars which reach supranuclear densities in their core. An accurate description of the neutron-matter equation of state is therefore crucial to describe these systems. To calculate the neutron-matter equation of state reliably, precise many-body methods in combination with a systematic theory for nuclear forces are needed. Chiral effective field theory (EFT) is such a theory. It provides a systematic framework for the description of low-energy hadronic interactions and enables calculations with controlled theoretical uncertainties. Chiral EFT makes use of a momentum-space expansion of nuclear forces based on the symmetries of Quantum Chromodynamics, which is the fundamental theory of strong interactions. In chiral EFT, the description of nuclear forces can be systematically improved by going to higher orders in the chiral expansion. On the other hand, continuum Quantum Monte Carlo (QMC) methods are among the most precise many-body methods available to study strongly interacting systems at finite densities. They treat the Schroedinger equation as a diffusion equation in imaginary time and project out the ground-state wave function of the system starting from a trial wave function by propagating the system in imaginary time. To perform this propagation, continuum QMC methods require as input local interactions. However, chiral EFT, which is naturally formulated in momentum space, contains several sources of nonlocality. In this Thesis, we show how to construct local chiral two-nucleon (NN) and three-nucleon (3N) interactions and discuss results of first QMC calculations for pure neutron systems. We have performed systematic auxiliary-field diffusion Monte Carlo (AFDMC) calculations for neutron matter using local chiral NN interactions. By
The moduli spaces of $3d$ ${\\cal N} \\ge 2$ Chern-Simons gauge theories and their Hilbert series
Cremonesi, Stefano; Zaffaroni, Alberto
2016-01-01
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\\cal N} \\ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of a residual gauge theory of massless fields in the monopole background. We provide a general formula for the case of abelian theories, where nonperturbative corrections are absent, and consider a few examples of nonabelian theories where nonperturbative corrections are well understood. We also analyze in detail nonabelian ABJ(M) theories as well as worldvolume theories of M2-branes probing Calabi-Yau fourfold and hyperK\\"ahler twofold singularities with ${\\cal N} = 2$ and ${\\cal N} = 3$ supersymmetry.
Anselmi, Damiano
2015-01-01
We prove the Adler-Bardeen theorem in a large class of general gauge theories, including nonrenormalizable ones. We assume that the gauge symmetries are general covariance, local Lorentz symmetry and Abelian and non-Abelian Yang-Mills symmetries, and that the local functionals of vanishing ghost number satisfy a variant of the Kluberg-Stern--Zuber conjecture. We show that if the gauge anomalies are trivial at one loop, for every truncation of the theory there exists a subtraction scheme where they manifestly vanish to all orders, within the truncation. Outside the truncation the cancellation of gauge anomalies can be enforced by fine-tuning local counterterms. The framework of the proof is worked out by combining a recently formulated chiral dimensional regularization with a gauge invariant higher-derivative regularization. If the higher-derivative regularizing terms are placed well beyond the truncation, and the energy scale $\\Lambda$ associated with them is kept fixed, the theory is super-renormalizable and...
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter we present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (orig.)
Mean field with corrections in lattice gauge theory
International Nuclear Information System (INIS)
A systematic expansion of the path integral for lattice gauge theory is performed around the mean field solution. In this letter the authors present the results for the pure gauge groups Z(2), SU(2) and SO(3). The agreement with Monte Carlo calculations is excellent. For the discrete group the calculation is performed with and without gauge fixing, whereas for the continuous groups gauge fixing is mandatory. In the case of SU(2) the absence of a phase transition is correctly signalled by mean field theory. (Auth.)
Applications of chiral perturbation theory to lattice QCD
Golterman, Maarten
2011-01-01
These notes contain the written version of lectures given at the 2009 Les Houches Summer School "Modern perspectives in lattice QCD: Quantum field theory and high performance computing." The goal is to provide a pedagogical introduction to the subject, and not a comprehensive review. Topics covered include a general introduction, the inclusion of scaling violations in chiral perturbation theory, partial quenching and mixed actions, chiral perturbation theory with heavy kaons, and the effects of finite volume, both in the p- and epsilon-regimes.
Vector and axial currents in Wilson chiral perturbation theory
International Nuclear Information System (INIS)
We reconsider the construction of the vector and axial-vector currents in Wilson Chiral Perturbation Theory, the low-energy effective theory for lattice QCD with Wilson fermions. We discuss in detail the finite renormalization of the currents that has to be taken into account in order to properly match the currents. We explicitly show that imposing the chiral Ward identities on the currents does, in general, affect the axial-vector current at O(a). As an application of our results we compute the pion decay constant to one loop in the two-flavor theory. Our result differs from previously published ones.
Disoriented chiral condensate: Theory and phenomenology
International Nuclear Information System (INIS)
These notes are an abbreviated version of lectures given at the 1997 Zakopane School. They contain two topics. The first is a description in elementary terms of the basic ideas underlying the speculative hypothesis that pieces of strong-interaction vacuum with a rotated chiral order parameter, disoriented chiral condensate or DCC, might be produced in high energy elementary particle collisions. The second topic is a discussion of the phenomenological techniques which may be applied to data in order to experimentally search for the existence of DCC
Heavy-tailed chiral random matrix theory
Kanazawa, Takuya
2016-01-01
We study an unconventional chiral random matrix model with a heavy-tailed probabilistic weight. The model is shown to exhibit chiral symmetry breaking with no bilinear condensate, in analogy to the Stern phase of QCD. We solve the model analytically and obtain the microscopic spectral density and the smallest eigenvalue distribution for an arbitrary number of flavors and arbitrary quark masses. Exotic behaviors such as non-decoupling of heavy flavors and a power-law tail of the smallest eigenvalue distribution are illustrated.
S-duality in N = 4 supersymmetric gauge theories with arbitrary gauge group
International Nuclear Information System (INIS)
The Goddard, Nuyts and Olive conjecture for electric-magnetic duality in the Yang-Mills theory with an arbitrary gauge group G is extended by including a non-vanishing vacuum angle θ. This extended S-duality conjecture includes the case when the unbroken gauge group in non-Abelian and a definite prediction for the spectrum of dyons results. (author)
3D SU(2) pure gauge theory in the maximally abelian gauge
International Nuclear Information System (INIS)
We investigate SU(2)3 lattice gauge theory in 3 Euclidean dimensions using maximally abelian gauge. We show that abelian monopole density is constant in continuum limit. The Creutz ratios produced from abelian Wilson loops are close to ordinary Creutz ratios. We find evident correlations between Creutz ratios and monopole density. (orig.)
Higgs phase in non-Abelian gauge theories
International Nuclear Information System (INIS)
A non-Abelian gauge theory involving scalar fields with non-tachyonic mass terms in the Lagrangian is considered, in order to construct a finite energy density trial vacuum for this theory. The usual scalar potential arguments suggest that the vacuum of such a theory would be in the perturbative phase. However, the obvious choices for a vacuum in this phase, the Axial gauge and the Coulomb gauge bare vacua, do not have finite energy densities even with an ultraviolet cutoff. Indeed, it is a non-trivial problem to construct finite energy density vacua for non-Abelian gauge theories and this is intimately connected with the gauge fixing degeneracies of these theories. Since the gauge fixing is achieved in the Unitary gauge, this suggests that the Unitary gauge bare vacuum might be a finite energy trial vacuum and, despite the form of the scalar potential, the vacuum of this theory might be in a Higgs phase rather than the perturbative phase
Stability of topological defects in chiral superconductors: London theory
International Nuclear Information System (INIS)
This paper examines the thermodynamic stability of chiral domain walls and vortices-topological defects which can exist in chiral superconductors. Using London theory it is demonstrated that at sufficiently small applied and chiral fields the existence of domain walls and vortices in the sample is not favored and the sample's configuration is a single domain. The particular chirality of the single-domain configuration is neither favored nor disfavored by the applied field. Increasing the field leads to an entry of a domain-wall loop or a vortex into the sample. The formation of a straight domain wall is never preferred in equilibrium. Values of the entry (critical) fields for both types of defects, as well as the equilibrium size of the domain-wall loop, are calculated. We also consider a mesoscopic chiral sample and calculate its zero-field magnetization, susceptibility, and a change in the magnetic moment due to a vortex or a domain-wall entry. We show that in the case of a soft domain wall whose energetics is dominated by the chiral current (and not by the surface tension) its behavior in mesoscopic samples is substantially different from that in the bulk case and can be used for a controllable transfer of edge excitations. The applicability of these results to Sr2RuO4 - a tentative chiral superconductor - is discussed.
General relativity and gauge gravity theories of higher order
International Nuclear Information System (INIS)
It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G∞4 as the local gauge symmetry group and the symmetrical tensor of rank two gμν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one
Beauty physics in lattice gauge theory
International Nuclear Information System (INIS)
We summarize the present status of lattice gauge theory computations of the leptonic decay constants fD and fB. The various sources of systematic errors are explained in a manner easily understood by the non-expert. The results obtained by the different groups are then systematically compared. As a result, we derive estimates for fD and fB in the quenched approximation through an appropriate combination of the data available from the different groups. Since we account for a possible lattice spacing dependence, the final errors are quite large. However, it is now well known how these uncertainties can be reduced. For the decay constant of heavy-light pseudoscalar mesons with masses of 1-2 GeV, an interesting comparison of a full QCD result with the corresponding simulation in the quenched approximation can be done. Effects of sea quarks of mass ms are below the statistical accuracy of these simulations. Related quantities, like B-parameters, the spectrum of beauty-hadrons and the breaking of the QCD string are discussed briefly. (orig.)
National Computational Infrastructure for Lattice Gauge Theory
Energy Technology Data Exchange (ETDEWEB)
Reed, Daniel, A
2008-05-30
In this document we describe work done under the SciDAC-1 Project National Computerational Infrastructure for Lattice Gauge Theory. The objective of this project was to construct the computational infrastructure needed to study quantim chromodynamics (QCD). Nearly all high energy and nuclear physicists in the United States working on the numerical study of QCD are involved in the project, as are Brookhaven National Laboratory (BNL), Fermi National Accelerator Laboratory (FNAL), and Thomas Jefferson National Accelerator Facility (JLab). A list of the serior participants is given in Appendix A.2. The project includes the development of community software for the effective use of the terascale computers, and the research and development of commodity clusters optimized for the study of QCD. The software developed as part of this effort is pubicly available, and is being widely used by physicists in the United States and abroad. The prototype clusters built with SciDAC-1 fund have been used to test the software, and are available to lattice guage theorists in the United States on a peer reviewed basis.
Wrapping effects in supersymmetric gauge theories
International Nuclear Information System (INIS)
Several perturbative computations of finite-size effects, performed on the gauge side of the AdS/CFT correspondence by means of superspace techniques, are presented. First, wrapping effects are analyzed in the standard N = 4 theory, by means of the calculation of the four-loop anomalous dimension of the Konishi operator. Then, a similar computation at five loops is described. Afterwards, finite-size effects are studied in the β-deformed case, where thanks to the reduced number of supersymmetries the simpler class of single-impurity operators can be considered, so that the leading corrections to the anomalous dimensions at generic order can be reduced to the computation of a class of integrals. Explicit results are given up to eleven loops. A further chapter is dedicated to the computation of the leading finite-size effects on operators dual to open strings. In the end, some comments are made and proposals for future developments are discussed. (Abstract Copyright [2010], Wiley Periodicals, Inc.)
Topological quantum field theories and gauge invariance in stochastic quantization
International Nuclear Information System (INIS)
The Langevin equations describing the quantization of gauge theories have a geometrical structure. We show that stochastically quantized gauge theories are governed by a single differential operator. The latter combines supersymmetry and ordinary gauge transformations. Quantum field theory can be defined on the basis of a Hamiltonian of the type H = 1/2[,Q-bar] where Q has deep relationship with the conserved BRST charge of a topological gauge theory, and Q-bar is its adjoint. We display the examples of Yang-Mills theory and of 2D gravity. Interesting applications are for first order actions, in particular for the theories defined by the three dimensional Chern Simons action as well as the ''two dimensional'' ∫M2TrΦF. (author). 15 refs
Gauge theory description of compactified pp-waves
International Nuclear Information System (INIS)
We find a new Penrose limit of AdS5xS5 that gives the maximally symmetric pp-wave background of type-IIB string theory in a coordinate system that has a manifest space-like isometry. This induces a new pp-wave/gauge-theory duality which on the gauge theory side involves a novel scaling limit of N=4 SYM theory. The new Penrose limit, when applied to AdS5xS5/ZM, yields a pp-wave with a space-like circle. The dual gauge theory description involves a triple scaling limit of an N=2 quiver gauge theory. We present in detail the map between gauge theory operators and string theory states including winding states, and verify agreement between the energy eigenvalues obtained from string theory and those computed in gauge theory, at least to one-loop order in the planar limit. We furthermore consider other related new Penrose limits and explain how these limits can be understood as part of a more general framework. (author)
SU(3) Chiral Symmetry in Non-Relativistic Field Theory
Ouellette, S M
2001-01-01
Applications imposing SU(3) chiral symmetry on non-relativistic field theory are considered. The first example is a calculation of the self-energy shifts of the spin-3/2 decuplet baryons in nuclear matter, from the chiral effective Lagrangian coupling octet and decuplet baryon fields. Special attention is paid to the self-energy of the delta baryon near the saturation density of nuclear matter. We find contributions to the mass shifts from contact terms in the effective Lagrangian with coefficients of unknown value. As a second application, we formulate an effecive field theory with manifest SU(2) chiral symmetry for the interactions of K and eta mesons with pions at low energy. SU(3) chiral symmetry is imposed on the effective field theory by a matching calculation onto three-flavor chiral perturbation theory. The effective Lagrangian for the pi-K and pi-eta sectors is worked out to order Q^4; the effective Lagrangian for the K-K sector is worked out to order Q^2 with contact interactions to order Q^4. As an...
Maps for currents and anomalies in noncommutative gauge theories
Banerjee, Rabin; Kumar, Kuldeep
2004-01-01
We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field approximation, these maps are also seen to connect the star-gauge-covariant anomaly in the noncommutative theory with the standard Adler--Bell--Jackiw anomaly in the commutative version. For arbitrary fields, derivative corrections to the maps are explicitly computed...
Perturbative Gravity and Gauge Theory Relations: A Review
Directory of Open Access Journals (Sweden)
Thomas Søndergaard
2012-01-01
Full Text Available This paper is dedicated to the amazing Kawai-Lewellen-Tye relations, connecting perturbative gravity and gauge theories at tree level. The main focus is on n-point derivations and general properties both from a string theory and pure field theory point of view. In particular, the field theory part is based on some very recent developments.
Quantization of higher abelian gauge theory in generalized differential cohomology
Szabo, R.
We review and elaborate on some aspects of the quantization of certain classes of higher abelian gauge theories using techniques of generalized differential cohomology. Particular emphasis is placed on the examples of generalized Maxwell theory and Cheeger-Simons cohomology, and of Ramond-Ramond fields in Type II superstring theory and differential K-theory.
SDiff gauge theory and the M2 condensate
Bandos, Igor A.; Townsend, Paul K.
2009-02-01
We develop a general formalism for the construction, in D-dimensional Minkowski space, of gauge theories for which the gauge group is the infinite-dimensional group SDiffn of volume-preserving diffeomorphisms of some closed n-dimensional manifold. We then focus on the D = 3 SDiff3 superconformal gauge theory describing a condensate of M2-branes; in particular, we derive its Script N = 8 superfield equations from a pure-spinor superspace action, and we describe its relationship to the D = 3 SDiff2 super-Yang-Mills theory describing a condensate of D2-branes.
Nonlocal Regularization For Non-Abelian Gauge Theories For Arbitrary Gauge Parameter
Basu, Anirban; Joglekar, Satish D.
2000-01-01
We study the nonlocal regularization for the non-abelian gauge theories for an arbitrary value of the gauge parameter (\\xi). We show that the procedure for the nonlocalization of field theories established earlier by the original authors, when applied in that form to the Faddeev-Popov effective action in a linear gauge cannot lead to a (\\xi)-independent result for the observables. We then show that an alternate procedure which is simpler can be used and that it leads to the S-matrix elements ...
Matrix product states for Hamiltonian lattice gauge theories
Buyens, Boye; Haegeman, Jutho; Verstraete, Frank
2014-01-01
Over the last decade tensor network states (TNS) have emerged as a powerful tool for the study of quantum many body systems. The matrix product states (MPS) are one particular case of TNS and are used for the simulation of 1+1 dimensional systems. In [1] we considered the MPS formalism for the simulation of the Hamiltonian lattice gauge formulation of 1+1 dimensional one flavor quantum electrodynamics, also known as the massive Schwinger model. We deduced the ground state and lowest lying excitations. Furthermore, we performed a full quantum real-time simulation for a quench with a uniform background electric field. In this proceeding we continue our work on the Schwinger model. We demonstrate the advantage of working with gauge invariant MPS by comparing with MPS simulations on the full Hilbert space, that includes numerous non-physical gauge variant states. Furthermore, we compute the chiral condensate and recover the predicted UV-divergent behavior.
Landau Theory and the Emergence of Chirality in Viral Capsids
Dharmavaram, Sanjay; Klug, William; Rudnick, Joseph; Bruinsma, Robijn
2016-01-01
We present a generalized Landau-Brazovskii theory for the solidification of chiral molecules on a spherical surface. With increasing sphere radius one encounters first intervals where robust achiral density modulations appear with icosahedral symmetry via first-order transitions. Next, one en- counters intervals where fragile but stable icosahedral structures still can be constructed but only by superposition of multiple irreducible representations. Chiral icoshedral structures appear via continuous or very weakly first-order transitions. Outside these parameter intervals, icosahedral symmetry is broken along a three-fold axis or a five-fold axis. The predictions of the theory are compared with recent numerical simulations.
Phase diagram of 4D field theories with chiral anomaly from holography
Ammon, Martin; Leiber, Julian; Macedo, Rodrigo P.
2016-03-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Phase diagram of 4D field theories with chiral anomaly from holography
Ammon, Martin; Macedo, Rodrigo P
2016-01-01
Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.
Oscillating cosmological solutions within gauge theories of gravity
Vereshchagin, G.
2003-01-01
New type of nonsingular oscillating solutions for the Universe described by cosmological equations of gauge theories of gravity is presented. Advantages of these solutions with respect to existing nonsingular solutions within framework of general relativity and gauge gravity are discussed. It is shown in particular that these solutions have nonzero measure and stable on contraction stage unlike usual nonsingular solutions.