The Third Way to 3D Gravity

TL;DR

This paper introduces a novel approach to 3D gravity, called the third way, which involves non-geometrical actions and resolves unitarity issues in topologically massive gravity, with potential applications beyond three dimensions.

Contribution

It proposes the third way to 3D gravity, a new method involving non-geometrical actions that addresses unitarity problems in topologically massive gravity.

Findings

Introduces the third way to 3D gravity.

Demonstrates resolution of unitarity issues in minimal massive gravity.

Suggests the third way's applicability to higher-dimensional theories.

Abstract

Consistency of Einstein's gravitational field equation $G_{\mu\nu} \propto T_{\mu\nu}$ imposes a "conservation condition" on the $T$-tensor that is satisfied by (i) matter stress tensors, as a consequence of the matter equations of motion, and (ii) identically by certain other tensors, such as the metric tensor. However, there is a third way, overlooked until now because it implies a "non-geometrical" action: one {\it not} constructed from the metric and its derivatives alone. The new possibility is exemplified by the 3D "minimal massive gravity" model, which resolves the "bulk vs. boundary" unitarity problem of topologically massive gravity with anti-de Sitter asymptotics. Although all known examples of the third way are in three spacetime dimensions, the idea is general and could, in principle, apply to higher-dimensional theories.