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Article
Report number	hep-th/9206010 ; CERN-TH-6471-92 ; HU-TFT-92-15 ; CERN-TH-6471-92 ; HU-TFT-92-15
Title	Index theorems and loop space geometry
Author(s)	Hietamaki, A. (Helsinki U.) ; Niemi, Antti J. (CERN)
Affiliation	(Univ. Helsinki) ; (CERN)
Publication	1992
Imprint	Apr 1992
Number of pages	11
In:	Phys. Lett. B 288 (1992) 331-341
DOI	10.1016/0370-2693(92)91111-L
Subject category	General Theoretical Physics
Abstract	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.
Copyright/License	Copyright @ unknown. Published by Elsevier B.V.

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