One-Loop Renormalization of Higher-Derivative 2D Dilaton Gravity

TL;DR

This paper introduces a higher-derivative 2D dilaton gravity theory inspired by string theory, calculates its one-loop divergences, and demonstrates the existence of black hole solutions within a renormalizable case.

Contribution

It proposes a new higher-derivative 2D dilaton gravity model, analyzes its one-loop divergences, and connects it to a D=2 sigma-model, revealing black hole solutions.

Findings

One-loop divergences calculated in covariant and conformal gauges.

The theory can be interpreted as a higher-derivative sigma-model.

Black hole solutions exist in the renormalizable case.

Abstract

A theory of higher-derivative 2D dilaton gravity which has its roots in the massive higher-spin mode dynamics of string theory is suggested. The divergences of the effective action to one-loop are calculated, both in the covariant and in the conformal gauge. Some technical problems which appear in the calculations are discussed. An interpretation of the theory as a particular D=2 higher-derivative $\sigma$-model is given. For a specific case of higher-derivative 2D dilaton gravity, which is one loop multiplicatively renormalizable, static configurations corresponding to black holes are shown to exist.