Supersymmetry and trace formulas. Part I. Compact Lie groups

Changha Choi (Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA) ; Leon Takhtajan (Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794, USA; Euler International Mathematical Institute, Pesochnaya Nab. 10, Saint Petersburg, 197022, Russia)

In the context of supersymmetric quantum mechanics we formulate new supersymmetric localization principle, with application to trace formulas for a full thermal partition function. Unlike the standard localization principle, this new principle allows to compute the supertrace of non-supersymmetric observables, and is based on the existence of fermionic zero modes. We describe corresponding new invariant supersymmetric deformations of the path integral; they differ from the standard deformations arising from the circle action and require higher derivatives terms. Consequently, we prove that the path integral localizes to periodic orbits and not only on constant ones. We illustrate the principle by deriving bosonic trace formulas on compact Lie groups, including classical Jacobi inversion formula.

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Published on:
05 June 2024
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2024 (2024)
Issue 6
Pages 1-38
DOI:
https://doi.org/10.1007/JHEP06(2024)026
arXiv:
2112.07942
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: