Supersymmetry and trace formulas. Part III. Frenkel trace formula

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].