Wess-Zumino terms and the geometry of the determinant line bundle

Abstract

The determinant line bundle L of a family of Dirac operators coupled to Yang-Mills (YM) in any dimension is constructed from the corresponding Wess-Zumino (WZ) term. The equivalence between the algebraic and topological approaches to anomalies is established by straightforward computation. As a by-product the first Chern class of L is expressed through the WZ term and the integrated anomaly is explicitly seen to play the role of a functioonal magnetic field on the gauge-orbit space.