Two-dimensional effective action for matter fields coupled to the dilaton

TL;DR

This paper revises the calculation of the one-loop effective action for matter fields coupled to the dilaton in two dimensions, deriving a covariant form that includes both invariant and anomalous terms, and analyzes finite temperature effects.

Contribution

It provides a new, covariant derivation of the one-loop effective action for scalar and spinor fields coupled to the dilaton in two dimensions, including finite temperature effects.

Findings

Effective action includes conformally invariant and anomalous terms

The scalar effective action is nonlocal and infrared finite

Finite temperature effects on the effective action are computed

Abstract

We revise the calculation of the one-loop effective action for scalar and spinor fields coupled to the dilaton in two dimensions. Applying the method of covariant perturbation theory for the heat kernel we derive the effective action in an explicitly covariant form that produces both the conformally invariant and the conformally anomalous terms.For scalar fields the conformally invariant part of the action is nonlocal. The obtained effective action is proved to be infrared finite. We also compute the one-loop effective action for scalar fields at finite temperature.