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Index Theorems play an important role in both mathematics and physics and are a classic example of the deep interplay between the two fields. We present new results for index theorems on manifolds with boundary and torsion. The computation is made possible by studying the quantum mechanics of a supersymmetric spinning particle living on the manifold of interest. In particular the bulk contribution to the index is calculated via a precise definition of functional integrals over all possible paths. The results may be tested via Killing--Yano duality which provides a relation between Dirac operators on manifolds with and without torsion.