Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation

Adler, Stephen L.; Bardeen, William A.

doi:10.1103/physrev.182.1517

Cited by 1,051 publications

(967 citation statements)

References 16 publications

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“…Now, using 3 At this point there is no need to make a distinction between primed and unprimed variables.…”

Section: A Virial Theoremmentioning

confidence: 99%

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Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Ordóñez

2016

Physica A: Statistical Mechanics and its Applications

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We derive anomalous equations of state for nonrelativistic 2D complex bosonic fields with contact interactions, using Fujikawa's path-integral approach to anomalies and scaling arguments. In the process, we derive an anomalous virial theorem for such systems. The methods used are easily generalizable for other 2D systems, including fermionic ones, and of different spatial dimensionality, all of which share a classical SO(2, 1) Schrödinger symmetry. The discussion is of a more formal nature and is intended mainly to shed light on the structure of anomalies in 2D many-body systems. The anomaly corrections to the virial theorem and equation of state -pressure relationship -may be identified as the Tan contact term. The practicality of these ideas rests upon being able to compute in detail the Fujikawa Jacobian that contains the anomaly. This and other conceptual issues, as well as some recent developments, are discussed at the end of the paper.

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“…Now, using 3 At this point there is no need to make a distinction between primed and unprimed variables.…”

Section: A Virial Theoremmentioning

confidence: 99%

“…They were discovered in particle physics, where the mandatory regularization and renormalization of quantum field theory spoiled some existing classical symmetries [1][2][3]. Anomalies may also occur in nonrelativistic systems, but they are less well known.…”

Section: Introductionmentioning

confidence: 99%

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Ordóñez

2016

Physica A: Statistical Mechanics and its Applications

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“…For N=1 SYM within the superspace approach it has been demonstrated [19] that the only possible anomaly is the supersymmetric extension of the standard Adler-Bardeen anomaly [20] and its explicit form is given in ref. [21,22].…”

Section: Gauge Anomalymentioning

confidence: 99%

Wilson renormalization group for supersymmetric gauge theories and gauge anomalies

Bonini

Vian

1998

Nuclear Physics B

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We extend the Wilson renormalization group (RG) to supersymmetric theories. As this regularization scheme preserves supersymmetry, we exploit the superspace technique. To set up the formalism we first derive the RG flow for the massless Wess-Zumino model and deduce its perturbative expansion. We then consider N=1 supersymmetric Yang-Mills and show that the local gauge symmetry -broken by the regularization-can be recovered by a suitable choice of the RG flow boundary conditions. We restrict our analysis to the first loop, the generalization to higher loops presenting no difficulty due to the iterative nature of the procedure. Furthermore, adding matter fields, we reproduce the one-loop supersymmetric chiral anomaly to the second order in the vector field.

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“…We shall show that the one-flavor 't Hooft model spontaneously breaks this discrete axial symmetry reproducing all the effects that in the continuum are due to the anomaly, while the two-flavor model exhibits a translationally invariant ground state preserving the discrete axial symmetry. The chiral anomaly [29] in the two-flavor model is realized on the lattice via the explicit breaking of the U A (1)-symmetry induced by the staggered fermions. We shall finally extrapolate to the continuum limit both the mass spectrum and the pertinent chiral condensates of the 't Hooft models by means of suitable "Padé approximants" [30].…”

Section: Introductionmentioning

confidence: 99%

“…If the regularization is gauge invariant, so that the vector currents are conserved, then the axial currents acquire the anomaly [29]. The axial currents associated to the SU (N c ) generators satisfy the anomaly equation for N f flavors [34] …”

Section: Introductionmentioning

confidence: 99%

Strongly coupled 't Hooft model on the lattice

Berruto¹

2000

Nuclear Physics B - Proceedings Supplements

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We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, large − N c -color QCD 2 , on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the QCD solitons.The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (N c −→ ∞) of the gauge model corresponds to the large spin limit (S −→ ∞) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.

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Absence of Higher-Order Corrections in the Anomalous Axial-Vector Divergence Equation

Cited by 1,051 publications

References 16 publications

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Path-integral Fujikawa’s approach to anomalous virial theorems and equations of state for systems with SO(2,1) symmetry

Wilson renormalization group for supersymmetric gauge theories and gauge anomalies

Strongly coupled 't Hooft model on the lattice

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