Dimensional deconstruction and Wess-Zumino-Witten terms
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{sub colors} = 3) of N = D = 5. The theory also has a Skyrme term with a fixed coefficient.
- Research Organization:
- Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC02-76CH03000
- OSTI ID:
- 15017361
- Report Number(s):
- FERMILAB-PUB-04-345-T; arXiv eprint number hep-th/0411157; TRN: US0605261
- Journal Information:
- Phys.Rev.D71:046002,2005, Journal Name: Phys.Rev.D71:046002,2005
- Country of Publication:
- United States
- Language:
- English
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