Induced Connections in Field Theory: The Odd-Dimensional Yang-Mills Case

Details Induced Connections in Field Theory: The Odd-Dimensional Yang-Mills Case Induced Connections in Field Theory: The Odd-Dimensional Yang-Mills Case

1994-05-27

arxiv.org/abs/hep-th/9405178v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages Plain-TeX, Freiburg THEP-94/12

Scientific paper

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

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