Dimensional Deconstruction and Wess-Zumino-Witten Terms

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.

29 pages, no figures; replacement fixes a typographical minus sign error in eq.(16), an errant normalization factor, and clarifies some discussion issues

References in corpus (7)

• Heterotic and Type I String Dynamics from Eleven Dimensions
• (De)Constructing Dimensions
• Gauge Invariant Effective Lagrangian for Kaluza-Klein Modes
• Natural Theories of Ultra-Low Mass PNGB's: Axions and Quintessence
• Topological Solitons from DeConstructed Extra Dimensions
• Bounding Gauged Skyrmion Masses
• Topology in the Bulk: Gauge Field Solitons in Extra Dimensions

Cited by in corpus (24)

• TASI Lectures on Solitons
• Meson Transition Form Factors in Light-Front Holographic QCD
• Anomaly mediated neutrino-photon interactions at finite baryon density
• Composite Accidental Axions
• T-Parity Violation by Anomalies
• Skyrmions from Instantons inside Domain Walls
• Standard Model Gauging of the WZW Term: Anomalies, Global Currents and pseudo-Chern-Simons Interactions
• Topological Physics of Little Higgs Bosons
• Stuckelberg Axions and the Effective Action of Anomalous Abelian Models 1. A unitarity analysis of the Higgs-axion mixing
• Windows over a New Low Energy Axion
• Anomalies, Chern-Simons Terms and Chiral Delocalization in Extra Dimensions
• Stuckelberg Axions and the Effective Action of Anomalous Abelian Models 2. A SU(3)_C x SU(2)_W x U(1)_Y x U(1)_B model and its signature at the LHC
• Trilinear Anomalous Gauge Interactions from Intersecting Branes and the Neutral Currents Sector
• Little Technicolor
• Exact Equivalence of the D=4 Gauged Wess-Zumino-Witten Term and the D=5 Yang-Mills Chern-Simons Term
• Photoproduction through Chern-Simons Term Induced Interactions in Holographic QCD
• Gauged Wess-Zumino terms for a general coset space
• Hadronic Form Factor Models and Spectroscopy Within the Gauge/Gravity Correspondence
• Quark and Lepton Masses from Deconstruction
• Pentaquarks, Skyrmions and the Vector Manifestation of Chiral Symmetry
• WZW action in odd dimensional gauge theories
• Anomaly inflow mechanism using Wilson line
• Topological physics in the standard model and beyond
• Chern-Simons and WZW Anomaly Cancelations Across Dimensions