Spinors on manifolds with boundary: APS index theorems with torsion

Index theorems for the Dirac operator allow one to study spinors on manifoldswith boundary and torsion. We analyse the modifications of the boundaryChern-Simons correction and APS eta invariant in the presence of torsion. Thebulk contribution must also be modified and is computed using a supersymmetricquantum mechanics representation. Here we find agreement with existing resultswhich employed heat kernel and Pauli-Villars techniques. Nonetheless, thiscomputation also provides a stringent check of the Feynman rules of de Boer etal. for the computation of quantum mechanical path integrals. Our results canbe verified via a duality relation between manifolds admitting a Killing-Yanotensor and manifolds with torsion. As an explicit example, we compute theindices of Taub-NUT and its dual constructed using this method and findagreement for any finite radius to the boundary. We also suggest a resolutionto the problematic appearance of the Nieh-Yan invariant multiplied by theregulator mass^2 in computations of the chiral gravitational anomaly coupled totorsion.Comment: 40 pages, LaTeX2e, uses feynmp.st