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

TL;DR

This paper investigates the holographic dual of the T\bar{T} deformation, emphasizing the importance of boundary terms in the gravity action and analyzing differences between holographic and field theory results on curved backgrounds.

Contribution

It clarifies the role of boundary terms in the holographic dual of T\bar{T} deformed CFTs and compares holographic predictions with field theory results on curved spaces.

Findings

Boundary term must be included in the gravity action for accurate holographic duality.

Differences are identified between holographic and field theory results on curved backgrounds.

Analysis on sphere and AdS backgrounds enhances understanding of T\bar{T} deformations.

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.