Exact equivalence of the D=4 gauged WessZuminoWitten term and the D=5 YangMills ChernSimons term
Abstract
We derive the full WessZuminoWitten term of a gauged chiral Lagrangian in D=4 by starting from a pure YangMills 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 ChernSimons 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 WessZuminoWitten term then emerges straightforwardly, from the YangMills ChernSimons term, plus boundary term. The method is systematic and allows generalization of the WessZuminoWitten term to theories of extra dimensions, and to express it in alternative and more compact forms. We give a novelmore »
 Authors:

 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 05562821
 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; YANGMILLS THEORY
Citation Formats
Hill, Christopher T. Exact equivalence of the D=4 gauged WessZuminoWitten term and the D=5 YangMills ChernSimons term. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.126009.
Hill, Christopher T. Exact equivalence of the D=4 gauged WessZuminoWitten term and the D=5 YangMills ChernSimons term. United States. https://doi.org/10.1103/PhysRevD.73.126009
Hill, Christopher T. Thu .
"Exact equivalence of the D=4 gauged WessZuminoWitten term and the D=5 YangMills ChernSimons term". United States. https://doi.org/10.1103/PhysRevD.73.126009.
@article{osti_20774954,
title = {Exact equivalence of the D=4 gauged WessZuminoWitten term and the D=5 YangMills ChernSimons term},
author = {Hill, Christopher T},
abstractNote = {We derive the full WessZuminoWitten term of a gauged chiral Lagrangian in D=4 by starting from a pure YangMills 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 ChernSimons 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 WessZuminoWitten term then emerges straightforwardly, from the YangMills ChernSimons term, plus boundary term. The method is systematic and allows generalization of the WessZuminoWitten 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 = {05562821},
number = 12,
volume = 73,
place = {United States},
year = {2006},
month = {6}
}