Comments on supersymmetric renormalization in two-dimensional curved spacetime

Abstract

In this technical note we introduce a manifestly gauge-invariant and supersymmetric procedure to regularize and renormalize one-loop divergences of chiral multiplets in two-dimensional N = (2, 2) theories in curved spacetime. We apply the method, a version of Pauli-Villars regularization, to known examples of supersymmetric localization and demonstrate that the partition functions are renormalized.