On the renormalization of higher derivative two dimensional gravity.

TL;DR

This paper demonstrates the equivalence of higher derivative two-dimensional gravity models to nonlinear sigma models with 2D quantum gravity, analyzing counterterms and auxiliary fields to understand renormalization.

Contribution

It explicitly shows the reduction of fourth derivative gravity models to sigma models with auxiliary fields and analyzes their counterterm structures.

Findings

Counterterms contain only second derivative structures

Explicit calculations performed in various gauges

Auxiliary fields facilitate the analysis of renormalization

Abstract

The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar fields and can be performed in an explicit way for both metric and general metric-dilaton cases. In view of this we can evaluate the structure of possible counterterms and show that they contains second derivative structures only. The calculations in the theory with an auxiliary fields require some special procedure to be applied. We perform the explicit calculations in a different gauges and explore the features of the auxiliary fields.