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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

Authors:
;
Publication Date:
Research Org.:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
892521
Report Number(s):
FERMILAB-PUB-06-046-T
arXiv eprint number hep-th/0603060
DOE Contract Number:
AC02-76CH03000
Resource Type:
Journal Article
Resource Relation:
Journal Name: Phys.Rev.D73:126009,2006
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Theory-HEP

Citation Formats

Hill, Christopher T., and /Fermilab. 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., & /Fermilab. Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term. United States. doi:10.1103/PhysRevD.73.126009.
Hill, Christopher T., and /Fermilab. Wed . "Exact equivalence of the D=4 gauged Wess-Zumino-Witten term and the D=5 Yang-Mills Chern-Simons term". United States. doi:10.1103/PhysRevD.73.126009. https://www.osti.gov/servlets/purl/892521.
@article{osti_892521,
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. and /Fermilab},
abstractNote = {},
doi = {10.1103/PhysRevD.73.126009},
journal = {Phys.Rev.D73:126009,2006},
number = ,
volume = ,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2006},
month = {Wed Mar 01 00:00:00 EST 2006}
}
  • 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,more » 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.« less
  • The standard model SU(2){sub L}xU(1){sub Y} gauging of the Wess-Zumino-Witten term requires a modified counterterm when background fields, needed to generate the full set of currents, are introduced. The modified counterterm plays an essential role in properly defining covariant global currents and their anomalies. For example, it is required in order to correctly derive the gauge-invariant baryon number current and its anomalous divergence. The background fields can also be promoted to a description of the physical spin-1 vector and axial-vector mesons in QCD and the counterterm leads to novel interactions. These are (pseudo)Chern-Simons terms, such as {epsilon}{sup {mu}}{sup {nu}}{sup {rho}}{supmore » {sigma}}{omega}{sub {mu}}Z{sub {nu}}{partial_derivative}{sub {rho}}A{sub {sigma}} and {epsilon}{sup {mu}}{sup {nu}}{sup {rho}}{sup {sigma}}{rho}{sub {mu}}{sup {+-}}W{sub {nu}}{sup {+-}}{partial_derivative}{sub {rho}}A{sub {sigma}} that mediate new interactions between neutrinos and photons at finite baryon density.« less
  • In this paper two things are done. First it is shown how a four-dimensional gauged Wess-Zumino-Witten term arises from the five-dimensional Einstein-Hilbert plus Gauss-Bonnet Lagrangian with a special choice of the coefficients. Second, the way in which the equations of motion of four-dimensional General Relativity arise is exhibited.
  • This paper reports on the coupling of the 2{ital n}-dimensional Wess--Zumino--Witten action to gauge fields discussed and a simple manifestly gauge-invariant form of the gauged Wess--Zumino term is found which is an integral over a (2{ital n} + 1)-dimensional space whose boundary is space-time. In two and four dimensions, our actions give simple forms for the action describing coset conformal field theories and the low-energy QCD effective action, respectively.
  • Two /ital Ansa/$/ital uml/---/ital tze/ for the gauge field potential are given so that the(2+1)-dimensional Yang-Mills equations with the Chern-Simons termcan be solved in terms of the modified Bessel functions and the ellipticfunction respectively.