Supersymmetry and trace formulas II. Selberg trace formula

By extending the new supersymmetric localization principle introduced in [2], 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.