Asymptotic T-duality in three dimensions

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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="fraktur"> <mml:mi>𝔟</mml:mi> <mml:mi>𝔪</mml:mi> <mml:mi>𝔰</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , \mathfrak{bms}_3 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mstyle mathvariant="fraktur"> <mml:mi>𝔟</mml:mi> <mml:mi>𝔪</mml:mi> <mml:mi>𝔰</mml:mi> </mml:mstyle> <mml:mn>3</mml:mn> </mml:msub> </mml:math> , 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 Compère-Song-Strominger ones.