Polyakov Effective Action from Functional Renormalization Group Equation

TL;DR

This paper derives the flow equation for the Polyakov effective action's form factor using the functional renormalization group, providing a non-local covariant truncation approach in two-dimensional curved space.

Contribution

It introduces a novel non-local covariant truncation of the effective average action and derives the flow equation for the form factor in the Polyakov effective action.

Findings

Derived the flow equation for the form factor in the effective action

Connected the flow from ultraviolet to infrared to recover standard results

Provided a new approach to analyze the Polyakov effective action in curved space

Abstract

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