3D gravity and double copy theory

TL;DR

This paper presents a new reformulation of 3D gravity using divergenceless vector frames, inspired by double copy concepts, offering geometric insights and connections to Chern-Simons theory.

Contribution

It introduces a novel on-shell equivalent formulation of 3D gravity based on divergenceless vector frames, inspired by double copy ideas, with links to Chern-Simons actions and higher-dimensional origins.

Findings

Reformulation provides a transparent geometric interpretation of double copy in 3D gravity.

Relates the new formulation to a Chern-Simons-like action.

Explores extensions leading to AdS3 geometry.

Abstract

We introduce a novel reformulation of three-dimensional gravity in terms of divergenceless vector frames, inspired by the double copy for Chern-Simons theory. This formulation is on-shell equivalent to conventional 3D gravity and provides a transparent geometric interpretation of the double-copy construction. We relate the resulting theory to a Chern-Simons-like action, propose a higher-dimensional origin, and explore extensions that give rise to $AdS_3$