Super heat kernel and one-loop divergence of super Yang–Mills theory in conformal supergravity

Abstract

Abstract We consider super Yang–Mills (SYM) theory in $N=1$ conformal supergravity. Using the background field method and the Faddeev–Popov procedure, the quantized action of the theory is presented. Its one-loop effective action is studied using the heat kernel method. We shall develop a non-iterative scheme, generalizing the non-supersymmetric case, to obtain the super heat kernel coefficients. In particular, the first three coefficients, which govern the one-loop divergence, will be calculated. We shall also demonstrate how to schematically derive the higher-order coefficients. The method presented here can be readily applied to various quantum theories. We shall, as an application, derive the full one-loop divergence of SYM in conformal supergravity.