Polyakov effective action from functional renormalization group equation

We discuss the Polyakov effective action for a minimally coupled scalar field on a two dimensional curved space by considering a non-local covariant truncation of the effective average action. We derive the flow equation for the form factor in integral root gRc(k)(Delta)R, and we show how the standard result is obtained when we integrate the flow from the ultraviolet to the infrared. (C) 2010 Elsevier Inc. All rights reserved.