On higher-derivative dilatonic gravity in two dimensions

TL;DR

This paper simplifies two-dimensional higher-derivative dilatonic gravity by mapping it to a multi-dilaton sigma-model coupled with Jackiw-Teitelboim gravity, and analyzes its quantum divergences and finiteness conditions.

Contribution

It introduces a method to reduce the order of 2D scalar-tensor $R^2$ gravity to a multi-dilaton model and computes the one-loop divergences for a specific degenerate case.

Findings

Derived the divergent part of the one-loop effective action.

Identified finiteness conditions for the model.

Mapped complex higher-derivative gravity to a simpler sigma-model framework.

Abstract

We discuss lowering the order of the two-dimensional scalar-tensor $R^2$ quantum gravity, by mapping the most general version of the model to a multi-dilaton gravity, which is essentially the sigma-model coupled with Jackiw-Teitelboim-like gravity. In the continuation of our previous research, we calculate the divergent part of the one-loop effective action in a 2D scalar-tensor (dilatonic) gravity with Ra2-term, which belongs to a specific degenerate case and cannot be obtained from the general expression. The corresponding finiteness conditions are found.