Holographic Action Principle for $T\bar{T}$-deformation

TL;DR

This paper develops a holographic action principle for the $Tar{T}$-deformation, successfully matching deformed Liouville theory actions on both field theory and gravity sides by incorporating the bending energy of the finite cut-off surface.

Contribution

It introduces a new holographic scheme that reproduces the $Tar{T}$-deformed action, including the bending energy of the cut-off surface, demonstrating a precise match between field theory and gravity.

Findings

Holographic scheme reproduces $Tar{T}$-deformed action.

Inclusion of bending energy of the cut-off surface is essential.

Perfect match between deformed actions on both sides.

Abstract

We explore the action principle for the holographic $T\bar{T}$-deformation. We develop a scheme in which one can holographically reproduce the action of the Liouville theory deformed by $T\bar{T}$-insertion. This scheme necessitates considering the bending energy of the finite cut-off surface. Following our proposal, one observes a perfect match between the actions of deformed theory on the field theory and gravity sides.