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Title: Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term

Abstract

We derive the full Wess-Zumino-Witten term of a gauged chiral Lagrangian in D=4 by starting from a pure Yang-Mills theory of gauged quark flavor in a flat, compactified D=5. The theory is compactified such that there exists a B{sub 5} zero mode, and supplemented with quarks that are 'chirally delocalized' with q{sub L} (q{sub R}) on the left (right) boundary (brane). The theory then necessarily contains a Chern-Simons term (anomaly flux) to cancel the fermionic anomalies on the boundaries. The constituent quark mass represents chiral symmetry breaking and is a bilocal operator in D=5 of the form: q{sub L}Wq{sub R}+h.c, where W is the Wilson line spanning the bulk, 0{<=}x{sup 5}{<=}R, and is interpreted as a chiral meson field, W=exp(2i{pi}-tilde/f{sub {pi}}), where f{sub {pi}}{approx}1/R. The quarks are integrated out, yielding a Dirac determinant which takes the form of a 'boundary term' (anomaly flux return), and is equivalent to Bardeen's counterterm that connects consistent and covariant anomalies. The Wess-Zumino-Witten term then emerges straightforwardly, from the Yang-Mills Chern-Simons term, plus boundary term. The method is systematic and allows generalization of the Wess-Zumino-Witten term to theories of extra dimensions, and to express it in alternative and more compact forms. We give a novelmore » form appropriate to the case of (unintegrated) massless fermions.« less

Authors:
 [1]
  1. Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 (United States)
Publication Date:
OSTI Identifier:
20774954
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 73; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.73.126009; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRAL SYMMETRY; CHIRALITY; COMPACTIFICATION; FLAVOR MODEL; LAGRANGIAN FUNCTION; MESONS; QUANTUM FIELD THEORY; QUARKS; REST MASS; SYMMETRY BREAKING; YANG-MILLS THEORY

Citation Formats

Hill, Christopher T. Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term. United States: N. p., 2006. Web. doi:10.1103/PhysRevD.73.126009.
Hill, Christopher T. Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term. United States. https://doi.org/10.1103/PhysRevD.73.126009
Hill, Christopher T. Thu . "Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term". United States. https://doi.org/10.1103/PhysRevD.73.126009.
@article{osti_20774954,
title = {Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term},
author = {Hill, Christopher T},
abstractNote = {We derive the full Wess-Zumino-Witten term of a gauged chiral Lagrangian in D=4 by starting from a pure Yang-Mills theory of gauged quark flavor in a flat, compactified D=5. The theory is compactified such that there exists a B{sub 5} zero mode, and supplemented with quarks that are 'chirally delocalized' with q{sub L} (q{sub R}) on the left (right) boundary (brane). The theory then necessarily contains a Chern-Simons term (anomaly flux) to cancel the fermionic anomalies on the boundaries. The constituent quark mass represents chiral symmetry breaking and is a bilocal operator in D=5 of the form: q{sub L}Wq{sub R}+h.c, where W is the Wilson line spanning the bulk, 0{<=}x{sup 5}{<=}R, and is interpreted as a chiral meson field, W=exp(2i{pi}-tilde/f{sub {pi}}), where f{sub {pi}}{approx}1/R. The quarks are integrated out, yielding a Dirac determinant which takes the form of a 'boundary term' (anomaly flux return), and is equivalent to Bardeen's counterterm that connects consistent and covariant anomalies. The Wess-Zumino-Witten term then emerges straightforwardly, from the Yang-Mills Chern-Simons term, plus boundary term. The method is systematic and allows generalization of the Wess-Zumino-Witten term to theories of extra dimensions, and to express it in alternative and more compact forms. We give a novel form appropriate to the case of (unintegrated) massless fermions.},
doi = {10.1103/PhysRevD.73.126009},
url = {https://www.osti.gov/biblio/20774954}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 12,
volume = 73,
place = {United States},
year = {2006},
month = {6}
}