Index Theorems and Loop Space Geometry

Details Index Theorems and Loop Space Geometry Index Theorems and Loop Space Geometry

1992-06-02

arxiv.org/abs/hep-th/9206010v1

Phys.Lett. B288 (1992) 331-341

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, report CERN-TH-6471 and HU-TFT-92-15

Scientific paper

10.1016/0370-2693(92)91111-L

We investigate the evaluation of the Dirac index using symplectic geometry in the loop space of the corresponding supersymmetric quantum mechanical model. In particular, we find that if we impose a simple first class constraint, we can evaluate the Callias index of an odd dimensional Dirac operator directly from the quantum mechanical model which yields the Atiyah-Singer index of an even dimensional Dirac operator in one more dimension. The effective action obtained by BRST quantization of this constrained system can be interpreted in terms of loop space symplectic geometry, and the corresponding path integral for the index can be evaluated exactly using the recently developed localization techniques.

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