Asymptotic T-duality in three dimensions

TL;DR

This paper explores how T-duality in three-dimensional gravity relates different solution spaces, revealing diverse asymptotic symmetries and connecting boundary conditions through duality transformations.

Contribution

It demonstrates how asymptotic T-duality maps phase spaces of solutions, uncovering new symmetry structures and linking different boundary conditions in three-dimensional gravity.

Findings

Asymptotic symmetry algebra includes bms_2, bms_3, and warped conformal algebra.

Duality relates Brown-Henneaux and Compere-Song-Strominger boundary conditions.

Large symmetry algebra for black string phase space.

Abstract

In (super)gravity theories, T-duality relates solutions with an exact isometry which can have wildly different asymptotic behaviors: a well-known example is the duality between BTZ black holes and (non-extremal) three-dimensional black strings. Using this dual pair, we show how the knowledge of a phase space which includes one set of solutions (here, BTZ black holes embedded in the Brown-Henneaux phase space) allows to obtain a phase space for the dual set via an asymptotic notion of T-duality. The resulting asymptotic symmetry algebras can be very different. For our particular example, we find a large algebra of symmetries for the black string phase space which includes as subalgebras $\mathfrak{bms}_2$, $\mathfrak{bms}_3$, and a twisted warped conformal algebra. On the way, we show that a chiral half of the Brown-Henneaux boundary conditions are dual to the Comp\`ere-Song-Strominger ones.