Holographic integration of $T \bar{T}$ and $J \bar{T}$ via $O(d,d)$

Abstract

Prompted by the recent developments in integrable single trace $T \bar{T}$ and $J \bar{T}$ deformations of 2d CFTs, we analyse such deformations in the context of $AdS_3/CFT_2$ from the dual string worldsheet CFT viewpoint. We observe that the finite form of these deformations can be recast as $O(d,d)$ transformations, which are an integrated form of the corresponding Exactly Marginal Deformations (EMD) in the worldsheet Wess-Zumino-Witten (WZW) model, thereby generalising the Yang-Baxter class that includes TsT. Furthermore, the equivalence between $O(d,d)$ transformations and marginal deformations of WZW models, proposed by Hassan and Sen for Abelian chiral currents, can be extended to non-Abelian chiral currents to recover a well-known constraint on EMD in the worldsheet CFT. We also argue that such EMD are also solvable from the worldsheet theory viewpoint.