Dual diffeomorphisms and finite distance asymptotic symmetries in 3d gravity

TL;DR

The paper identifies a two-dimensional space of well-defined quadratic charges in the most general first-order 3D gravity, corresponding to diffeomorphisms and a dual diffeomorphism. Through a Sugawara construction on the J–T current algebra, these generate a double Witt algebra at finite distance, with a flat limit yielding centreless BMS3; the work also connects these finite-distance charges to asymptotic Bondi charges, revealing a deep link between tangent diffeomorphisms and null directions via dual charges. The results illuminate how asymptotic Virasoro structures emerge from underlying current algebras without imposing boundary conditions, and outline future routes to central extensions and non-tangent generalizations. It also provides explicit Lagrangian, phase-space, and geometric structures (including explicit triad/connection) to support these conclusions.

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.