On-shell action of $\text{T}\bar{\text{T}}$-deformed Holographic CFTs

Abstract

In this work, we study the holographic dual of the $\text{T}\bar{\text{T}}$ deformation following the mixed boundary condition proposal. We point out that a boundary term should be included in the gravity action in the holographic dictionary. In particular, we consider the deformed CFT defined on a sphere (dS) or AdS background and explain the difference between the holographic results and field theory results.

title changed, the discussion about entanglement entropy is removed, which will be merged with another incoming e-print