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Axial anomalies of Lifshitz fermions

We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing wi...

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Detalles Bibliográficos
Autores principales: Bakas, Ioannis, Lust, Dieter
Lenguaje:eng
Publicado: 2011
Materias:
Acceso en línea:https://dx.doi.org/10.1002/prop.201100048
http://cds.cern.ch/record/1341194
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author Bakas, Ioannis
Lust, Dieter
author_facet Bakas, Ioannis
Lust, Dieter
author_sort Bakas, Ioannis
collection CERN
description We compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2)xU(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Horava-Lifshitz theory arising at lambda = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non-relativistic quantum field theories are also discussed.
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spelling cern-13411942019-09-30T06:29:59Zdoi:10.1002/prop.201100048http://cds.cern.ch/record/1341194engBakas, IoannisLust, DieterAxial anomalies of Lifshitz fermionsParticle Physics - TheoryWe compute the axial anomaly of a Lifshitz fermion theory with anisotropic scaling z=3 which is minimally coupled to geometry in 3+1 space-time dimensions. We find that the result is identical to the relativistic case using path integral methods. An independent verification is provided by showing with spectral methods that the eta-invariant of the Dirac and Lifshitz fermion operators in three dimensions are equal. Thus, by the integrated form of the anomaly, the index of the Dirac operator still accounts for the possible breakdown of chiral symmetry in non-relativistic theories of gravity. We apply this framework to the recently constructed gravitational instanton backgrounds of Horava-Lifshitz theory and find that the index is non-zero provided that the space-time foliation admits leaves with harmonic spinors. Using Hitchin's construction of harmonic spinors on Berger spheres, we obtain explicit results for the index of the fermion operator on all such gravitational instanton backgrounds with SU(2)xU(1) isometry. In contrast to the instantons of Einstein gravity, chiral symmetry breaking becomes possible in the unimodular phase of Horava-Lifshitz theory arising at lambda = 1/3 provided that the volume of space is bounded from below by the ratio of the Ricci to Cotton tensor couplings raised to the third power. Some other aspects of the anomalies in non-relativistic quantum field theories are also discussed.arXiv:1103.5693LMU-ASC 07-11MPP-2011-35CERN-PH-TH-2011-051oai:cds.cern.ch:13411942011-03-30
spellingShingle Particle Physics - Theory
Bakas, Ioannis
Lust, Dieter
Axial anomalies of Lifshitz fermions
title Axial anomalies of Lifshitz fermions
title_full Axial anomalies of Lifshitz fermions
title_fullStr Axial anomalies of Lifshitz fermions
title_full_unstemmed Axial anomalies of Lifshitz fermions
title_short Axial anomalies of Lifshitz fermions
title_sort axial anomalies of lifshitz fermions
topic Particle Physics - Theory
url https://dx.doi.org/10.1002/prop.201100048
http://cds.cern.ch/record/1341194
work_keys_str_mv AT bakasioannis axialanomaliesoflifshitzfermions
AT lustdieter axialanomaliesoflifshitzfermions