Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity

TL;DR

This paper explores the boundary symmetry algebra in 3D gravity, revealing a duality that extends the usual asymptotic symmetries to include dual diffeomorphisms, forming either a double Witt or BMS3 algebra.

Contribution

It introduces the concept of dual diffeomorphisms in 3D gravity and shows they form an extended symmetry algebra alongside traditional diffeomorphisms.

Findings

Dual diffeomorphisms form a symmetry algebra with diffeomorphisms.

The combined algebra is either a double Witt or BMS3 algebra.

A duality between null and angular directions underpins the extended symmetry.

Abstract

We study the finite distance boundary symmetry current algebra of the most general first order theory of 3d gravity. We show that the space of quadratic generators contains diffeomorphisms but also a notion of dual diffeomorphisms, which together form either a double Witt or centreless BMS$_3$ algebra. The relationship with the usual asymptotic symmetry algebra relies on a duality between the null and angular directions, which is possible thanks to the existence of the dual diffeomorphisms.