$T\bar{T}$-Deformations of Holographic Warped CFTs

We explore $T\bar{T}$ deformations of Warped Conformal Field Theories (WCFTs) in two dimensions as examples of $T\bar{T}$ deformed non-relativistic quantum field theories. WCFTs are quantum field theories with a Virasoro$\times$U(1) Kac-Moody symmetry. We compute the deformed symmetry algebra of a $T\bar{T}$ deformed holographic WCFT, using the asymptotic symmetries of AdS${}_3$ with $T\bar{T}$ deformed Compére, Song and Strominger (CSS) boundary conditions. The U(1) Kac-Moody symmetry survives provided one allows the boundary metric to transform under the asymptotic symmetry. The Virasoro sector remains but is now deformed and no longer chiral.