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 $\int \sqrt{g}R{c}_k(\mathrm{\Delta })R$, and we show how the standard result is obtained when we integrate the flow from the ultraviolet to the infrared.