This paper derives an exact path-integral formula for a left-right translated heat kernel trace on a compact semisimple Lie group, generalizing Frenkel's trace formula.
Supersymmetry and trace formulas II. Selberg trace formula
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abstract
By extending the new supersymmetric localization principle introduced in \cite{Choi:2021yuz}, we present a path integral derivation of the Selberg trace formula on arbitrary compact Riemann surfaces, including the case of vector-valued automorphic forms of arbitrary half-integer weight corresponding to Maass Laplacian. We also generalize the method to formulate the Selberg trace formula on generic compact locally symmetric space.
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Supersymmetry and trace formulas III. Frenkel trace formula
This paper derives an exact path-integral formula for a left-right translated heat kernel trace on a compact semisimple Lie group, generalizing Frenkel's trace formula.