Dimensional deconstruction and Wess-Zumino-Witten terms
- Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, Illinois 60510 (United States)
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 N{sub colors}=3) of N=D=5. The theory also has a Skyrme term with a fixed coefficient.
- OSTI ID:
- 20706058
- Journal Information:
- Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 4 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
CHIRAL SYMMETRY
CHIRALITY
COMMUTATORS
COMPACTIFICATION
CURRENT ALGEBRA
GAUGE INVARIANCE
LAGRANGIAN FIELD THEORY
LAGRANGIAN FUNCTION
LATTICE FIELD THEORY
NONLINEAR PROBLEMS
PSEUDOSCALAR MESONS
SKYRME POTENTIAL
SOLITONS
TOPOLOGY
UNITARY SYMMETRY
YANG-MILLS THEORY