T(T)over-bar/J(T)over-bar-deformed WZW models from Chern-Simons AdS3 gravity with mixed boundary conditions

In this work we consider AdS(3) gravitational theory with certain mixed boundary conditions at infinity. Using the Chem-Simons formalism of AdS(3) gravity, we find that these mixed boundary conditions lead to nontrivial boundary terms, which, in turn, produce exactly the spectrum of the T (T) over bar /J (T) over bar -deformed conformal field theories (CFTs). We then follow the procedure for constructing asymptotic boundary dynamics of AdS(3) to derive the constrained T (T) over bar -deformed Wess-Zumino-Witten (WZW) model from Chern-Simons gravity. The resulting theory turns out to be the T (T) over bar -deformed Alekseev-Shatashvili action after disentangling the constraints. Furthermore, by adding a U(1) gauge field associated to the current J, we obtain one type of the J (T) over bar -deformed WZW model, and show that its action can also be constructed from the gravity side. These results provide a check on the correspondence between the T (T) over bar /J (T) over bar -deformed CFTs and the deformations of boundary conditions of AdS(3), the latter of which may be regarded as coordinate transformations.

Automated summary

In this work, mixed boundary conditions in AdS(3) gravitational theory are considered, leading to nontrivial boundary terms and providing the spectrum of T (T) over bar /J (T) over bar -deformed CFTs. By using the Chern-Simons formalism of AdS(3) gravity, the constrained T (T) over bar -deformed Wess-Zumino-Witten (WZW) model is derived, which is shown to be the T (T) over bar -deformed Alekseev-Shatashvili action after disentangling the constraints. Additionally, a J (T) over bar -deformed WZW model is obtained by adding a U(1) gauge field associated to the current J, and its action can also be constructed from the gravity side.