One-loop Effective Action for a Generic 2D Dilaton Gravity Theory

TL;DR

This paper derives an explicit one-loop effective action for a broad class of 2D dilaton gravity theories, including the CGHS model and spherically symmetric GR, using the background-field method and large-N approximation.

Contribution

It provides a general expression for the one-loop effective action in 2D dilaton gravity with matter fields, extending previous specific models.

Findings

Explicit effective action in the weak-coupling limit.

Application to CGHS and spherically symmetric GR.

Large-N limit yields Polyakov-Liouville form.

Abstract

We study the one-loop effective action for a generic two-dimensional dilaton gravity theory conformally coupled to $N$ matter fields. We obtain an explicit expression for the effective action in the weak-coupling limit under a suitable restriction of the dilaton potential asymptotics. Our result applies to the CGHS model as well as to the spherically symmetric general relativity. The effective action is obtained by using the background-field method, and we take into account the loop contributions from all the fields in the classical action and from the ghosts. In the large-$N$ limit, and after an appropriate field redefinition, the one-loop correction takes the form of the Polyakov-Liouville action.