$T\bar{T}$ deformation of chiral bosons and Chern-Simons AdS$_3$ gravity

Understand

We study the $T\bar{T}$ deformation of the chiral bosons and show the equivalence between the chiral bosons of opposite chiralities and the scalar fields at the Hamiltonian level under the deformation.

• We also derive the deformed Lagrangian of more generic theories which contain an arbitrary number of chiral bosons to all orders.
• By using these results, we derive the $T\bar{T}$ deformed boundary action of the AdS$_3$ gravity theory in the Chern-Simons formulation.
• We compute the deformed one-loop torus partition function, which satisfies the $T\bar{T}$ flow equation up to the one-loop order.