Nonperturbative path integral of 2d dilaton gravity and two-loop effects from scalar matter

TL;DR

This paper performs a nonperturbative path integral in 2d dilaton gravity, incorporating two-loop quantum effects from scalar matter, resulting in a renormalized dilaton potential while maintaining an exact geometric action.

Contribution

It introduces a method to include two-loop quantum corrections from scalar matter into the nonperturbative path integral of 2d dilaton gravity, revealing a renormalized dilaton potential.

Findings

Quantum effects yield a correction to the Polyakov term.

The effective action experiences only a renormalization of the dilaton potential.

The geometric part of the action remains exact despite quantum corrections.

Abstract

Performing an nonperturbative path integral for the geometric part of a large class of 2d theories without kinetic term for the dilaton field, the quantum effects from scalar matter fields are treated as a perturbation. When integrated out to two-loops they yield a correction to the Polyakov term which is still exact in the geometric part. Interestingly enough the effective action only experiences a renormalization of the dilaton potential.