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<p>By applying the new supersymmetric localization principle introduced in [<CitationRef CitationID="CR5">5</CitationRef>, <CitationRef CitationID="CR6">6</CitationRef>], we present two complementary approaches for the path integral derivation of the ‘non-chiral’ trace formula for a semisimple compact Lie group <i>G</i>, which generalizes the so-called Frenkel trace formula. Corresponding physical systems for each picture are the quantum mechanical sigma model on <i>G</i> and the gauged sigma model on <i>G</i> × <i>G</i>, and the approaches closely follow the spirit of the Eskin trace formula [<CitationRef CitationID="CR5">5</CitationRef>] and the Selberg trace formula [<CitationRef CitationID="CR6">6</CitationRef>] respectively. These methods provide a natural conceptual bridge between two seemingly independent derivations in [<CitationRef CitationID="CR5">5</CitationRef>, <CitationRef CitationID="CR6">6</CitationRef>].</p>

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Supersymmetry and trace formulas. Part III. Frenkel trace formula

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月18日

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  • Changha Choi,
  • Leon A. Takhtajan

摘要

By applying the new supersymmetric localization principle introduced in [5, 6], 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 × G, and the approaches closely follow the spirit of the Eskin trace formula [5] and the Selberg trace formula [6] respectively. These methods provide a natural conceptual bridge between two seemingly independent derivations in [5, 6].