Dimensional deconstruction and Wess-Zumino-Witten terms

A new technique is developed for the derivation of the Wess-Zumino-Witten (WZW) terms of gauged chiral Lagrangians. We start in $D=5$ with a pure (mesonless) Yang-Mills theory, which includes relevant gauge field Chern-Simons terms. The theory is then compactified, and the effective $D=4$ Lagrangian is derived using lattice techniques, or ``deconstruction,'' where pseudoscalar mesons arise from the lattice Wilson links. This yields the WZW term with the correct Witten coefficient by way of a simple heuristic argument. We discover a novel WZW term for singlet currents, that yields the full Goldstone-Wilczek current, and a $U(1)$ axial current for the Skyrmion, with the appropriate anomaly structures. A more detailed analysis is presented of the dimensional compactification of Yang-Mills in $D=5$ into a gauged chiral Lagrangian in $D=4$, heeding the consistency of the $D=4$ and $D=5$ Bianchi identities. These dictate a novel covariant derivative structure in the $D=4$ gauge theory, yielding a field strength modified by the addition of commutators of chiral currents. The Chern-Simons term of the pure $D=5$ Yang-Mills theory then devolves into the correct form of the Wess-Zumino-Witten term with an index (the analogue of Ncolors=3) of $N=D=5$. The theory also has a Skyrme term with a fixed coefficient.