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

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-5 zero mode, and supplemented with quarks that are chirally delocalized with q(L) (q(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) over bar (L)Wq(R)+h.c, where W is the Wilson line spanning the bulk, 0 <= x(5)<= R, and is interpreted as a chiral meson field, W=exp(2i pi/f(pi)), where f(pi)similar to 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.