Dimensional Deconstruction and Wess-Zumino-Witten Terms

TL;DR

This paper introduces a new method for deriving Wess-Zumino-Witten terms in gauged chiral Lagrangians by starting from a five-dimensional Yang-Mills theory and using lattice deconstruction, revealing novel terms and anomaly structures.

Contribution

It develops a novel deconstruction technique from 5D Yang-Mills to 4D chiral Lagrangians, deriving WZW terms with correct coefficients and discovering new anomaly-related terms.

Findings

Derived WZW term with correct Witten coefficient

Discovered a novel WZW term for singlet currents

Identified a modified covariant derivative structure in 4D

Abstract

A new technique is developed for the derivation of the Wess-Zumino-Witten 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 N_{colors}=3) of N=D=5. The theory also has a Skyrme term with a fixed coefficient.