Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-01-05
JHEP 9902 (1999) 024
Physics
High Energy Physics
High Energy Physics - Theory
40 pages, LaTeX2e, uses feynmp.sty
Scientific paper
10.1088/1126-6708/1999/02/024
Index theorems for the Dirac operator allow one to study spinors on manifolds with boundary and torsion. We analyse the modifications of the boundary Chern-Simons correction and APS eta invariant in the presence of torsion. The bulk contribution must also be modified and is computed using a supersymmetric quantum mechanics representation. Here we find agreement with existing results which employed heat kernel and Pauli-Villars techniques. Nonetheless, this computation also provides a stringent check of the Feynman rules of de Boer et al. for the computation of quantum mechanical path integrals. Our results can be verified via a duality relation between manifolds admitting a Killing-Yano tensor and manifolds with torsion. As an explicit example, we compute the indices of Taub-NUT and its dual constructed using this method and find agreement for any finite radius to the boundary. We also suggest a resolution to the problematic appearance of the Nieh-Yan invariant multiplied by the regulator mass^2 in computations of the chiral gravitational anomaly coupled to torsion.
Peeters Kasper
Waldron Andrew
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