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arXiv · 2502.10210

Supersymmetry and trace formulas III. Frenkel trace formula

Changha Choi·Leon A. Takhtajan
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Abstract

By applying the new supersymmetric localization principle introduced in \cite{Choi:2021yuz,Choi:2023pjn}, we present two complementary approaches for the path integral derivation of the `non-chiral' trace formula for a semisimple compact Lie group $G$, which generalizes the so-called Frenkel trace formula. Corresponding physical systems for each picture are the quantum mechanical sigma model on $G$ and the gauged sigma model on $G\times G$, and the approaches closely follow the spirit of the Eskin trace formula \cite{Choi:2021yuz} and the Selberg trace formula \cite{Choi:2023pjn} respectively. These methods provide a natural conceptual bridge between two seemingly independent derivations in \cite{Choi:2021yuz} and \cite{Choi:2023pjn}.

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Changha Choi, Leon A. Takhtajan. 2025-02-14. Supersymmetry and trace formulas III. Frenkel trace formula. https://doi.org/10.1007/jhep06(2026)200

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