INDUCED CONNECTIONS IN FIELD THEORY: THE ODD-DIMENSIONAL YANG–MILLS CASE

Abstract

We consider SU(N) Yang–Mills theories in (2n + 1)-dimensional Euclidean space–time, where N ≥ n+1, coupled to an even flavor number of Dirac fermions. After integration over the fermionic degrees of freedom, the wave functional for the gauge field inherits a nontrivial U(1) connection which we compute in the limit of infinite fermion mass. Its Chern class turns out to be just half the flavor number, so that the wave functional now becomes a section in a nontrivial complex line bundle. The topological origin of this phenomenon is explained in both the Lagrangian and the Hamiltonian picture.