Supersymmetry and trace formulas II. Selberg trace formula

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 arbitrary vector-valued automorphic form and weight corresponding to Maass Laplacian. We also generalize the method to formulate the Selberg trace formula on generic compact locally symmetric space.