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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2502.10210 |
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| _version_ | 1866909516105252864 |
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| author | Choi, Changha Takhtajan, Leon A. |
| author_facet | Choi, Changha Takhtajan, Leon A. |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10210 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supersymmetry and trace formulas III. Frenkel trace formula Choi, Changha Takhtajan, Leon A. High Energy Physics - Theory Differential Geometry Representation Theory 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}. |
| title | Supersymmetry and trace formulas III. Frenkel trace formula |
| topic | High Energy Physics - Theory Differential Geometry Representation Theory |
| url | https://arxiv.org/abs/2502.10210 |