A new 2D formulation of modified General Relativity

TL;DR

This paper introduces a novel 2D formulation of modified General Relativity that results in well-defined field equations without extra scalar fields, breaking diffeomorphism invariance but clarifying previous methods.

Contribution

It presents an intrinsically two-dimensional Einstein action approach yielding new field equations, explaining prior methods and avoiding additional scalar fields or conformal transformations.

Findings

New 2D Einstein action yields non-trivial gravity models

Field equations break diffeomorphism invariance

Including conformal counter terms leads to equivalent results

Abstract

It is well known that the Einstein-Hilbert action in two dimensions is topological and yields an identically vanishing Einstein tensor. Consequently one is faced with difficulties when formulating a non-trivial gravity model. We present a new, intrinsically two-dimensional, approach to this problem based on the Einstein action. This yields a well defined variational approach which results in new field equations that break diffeomorphism invariance. Our proposed approach does not require the introduction of additional scalar fields, nor the use of conformal transformations. However, we can show how including conformal counter terms leads to equivalent results. In doing so, we can provide an explanation for why previous approaches worked. Solutions to the field equations are briefly discussed.