2006/03/10 by Christopher T. Hill
Physics and Astronomy · #Black Holes and Theoretical Physics #Mathematical physics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quark #hep-th
paper · pdf · doi:10.1103/physrevd.73.126009
published as Phys.Rev.D73:126009,2006 · 25 pages, 1 figure; minor errors fixed
arxiv created 2006/03/10 · openalex publication_date 2006/06/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 B5 zero mode, and supplemented with quarks that are ``chirally delocalized'' with qL (qR) 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: qLWqR+h.c, where W is the Wilson line spanning the bulk, 0\ensuremath≤x5\ensuremath≤R, and is interpreted as a chiral meson field, W=exp(2i\stackrel\texttildelow\ensuremathπ/f_\ensuremathπ), where f_\ensuremathπ\ensuremath∼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.