Phases of chiral gauge theories
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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...
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
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
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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.
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
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
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)
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
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.
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...
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
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
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
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)
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).
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
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
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
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.)
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...
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...
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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
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
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.
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
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
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
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
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
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
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?
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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...
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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).