Holonomy and the Wess-Zumino term
type: Item
instance of: scholarly article
title: Holonomy and the Wess-Zumino term
zbMATH Open document ID: 0623.58027
DOI: 10.1007/BF00402666
published in: Letters in Mathematical Physics
publication date: 1986-01-01T00:00:00Z
review text: If M is a manifold, Z a \((d-1)\)-dimensional manifold, and \(h\in C^{\infty}(S^ 1\times Z,M)\), the Wess-Zumino term \(\Gamma_{wz}(h)\) of h is defined by \(\Gamma_{wz}(h)=\exp \int_{H(D\times Z)}\omega\), where \(\omega/2\pi i\) is any integral closed \((d+1)\)-form, and \(H: D\times Z\to M\) is any smooth extension of h (D the unit disc). The authors show that the Wess-Zumino term of h can be interpreted as a holonomy term, i.e. the holonomy of some suitable curvature 2-form on \(C^{\infty}(Z,M)\) along \(\hat h:\) \(S^ 1\to C^{\infty}(Z,M)\), where \(\hat h(\theta)\)(z)\(=h(\theta,z)\).
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 81T99
Mathematics Subject Classification ID: 58D15
Mathematics Subject Classification ID: 53C05
Mathematics Subject Classification ID: 22E65
zbMATH DE Number: 4011488
zbMATH Keywords: Wess-Zumino term
zbMATH Keywords: holonomy term
author: A. L. Carey
author: Michael K. Murray
MaRDI profile type: Publication
cites work: Topological quantization and cohomology
cites work: On Some Recent Interactions Between Mathematics and Physics
cites work: Non-Abelian bosonization in two dimensions
description: scientific article; zbMATH DE number 4011488