Holographic $T\bar{T}$ deformation of the entanglement entropy in (A)dS$_3$/CFT$_2$

TL;DR

This paper extends the understanding of $Tar{T}$ deformations in holography, deriving analytical entanglement entropy formulas for (A)dS$_3$/CFT$_2$ and revealing non-locality in dual theories through strong subadditivity analysis.

Contribution

It generalizes the replica method for entanglement entropy in $Tar{T}$-deformed holography and analytically extends the trace flow equation from AdS to dS spacetime.

Findings

Derived analytical entanglement entropy expressions for finite size and temperature systems.

Extended the trace flow equation from AdS to dS spacetime via double Wick rotations.

Identified non-locality in dual field theories through strong subadditivity analysis.

Abstract

In recent years, the holographic duality between $T\bar{T}$-deformed conformal field theory (CFT) and Anti-de Sitter (AdS) spacetime with finite radial cutoff has received significant attention. The study of $T\bar{T}$ deformation within the framework of de Sitter (dS)/CFT duality has also progressed. This paper shows that the trace flow equation in dS spacetime can be analytically extended from its AdS counterpart through double Wick rotations. Meanwhile, we generalize the replica method in both AdS and dS holography to derive a general expression for the entanglement entropy of arbitrary single spatial intervals within the $T\bar{T}$-deformed framework. For both finite size and finite temperature systems, we obtain the analytical expression for the entanglement entropy after $T\bar{T}$ deformation. Finally, in dS/dS holography and half-dS holography, we find that the dual field theory exhibits non-locality by analyzing the strong subadditivity and boosted strong subadditivity of entanglement entropy.