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Holographic $T\bar{T}$ deformed entanglement entropy in dS$_3$/CFT$_2$

Deyou Chen, Xin Jiang, Haitang Yang

TL;DR

This work analyzes holographic entanglement in the $T\bar{T}$-deformed version of the dS$_3$/CFT$_2$ correspondence by computing the pseudoentropy for a two-antipodal-points entangling surface on $\mathbb{S}^2$ and showing it exactly equals the complex geodesic length in the dS$_3$ bulk. It employs the Wheeler-DeWitt framework and the $T\bar{T}$ flow to relate boundary deformations to a finite-time bulk cutoff, with imaginary central charge $c = -i c_{\mathrm{dS}}$ and imaginary deformation parameter $\lambda = -i \lambda_{\mathrm{dS}}$. The key result is a precise match between the boundary pseudoentropy, $S_A = \frac{\pi c_{\mathrm{dS}}}{6} - i \frac{c_{\mathrm{dS}}}{3} t$, and the bulk complex geodesic RT length, reinforcing the consistency of dS$_3$/CFT$_2$ with a finite-time holographic picture even in a non-unitary setting. This advances the understanding of holographic entanglement in de Sitter spacetimes and demonstrates the utility of $T\bar{T}$ deformations in connecting boundary QFT observables to bulk geometric quantities.

Abstract

In this paper, based on the $T\bar{T}$ deformed version of $\text{dS}_3/\text{CFT}_2$ correspondence, we calculate the pseudoentropy for an entangling surface consisting of two antipodal points on a sphere and find it is exactly dual to the complex geodesic in the bulk.

Holographic $T\bar{T}$ deformed entanglement entropy in dS$_3$/CFT$_2$

TL;DR

This work analyzes holographic entanglement in the -deformed version of the dS/CFT correspondence by computing the pseudoentropy for a two-antipodal-points entangling surface on and showing it exactly equals the complex geodesic length in the dS bulk. It employs the Wheeler-DeWitt framework and the flow to relate boundary deformations to a finite-time bulk cutoff, with imaginary central charge and imaginary deformation parameter . The key result is a precise match between the boundary pseudoentropy, , and the bulk complex geodesic RT length, reinforcing the consistency of dS/CFT with a finite-time holographic picture even in a non-unitary setting. This advances the understanding of holographic entanglement in de Sitter spacetimes and demonstrates the utility of deformations in connecting boundary QFT observables to bulk geometric quantities.

Abstract

In this paper, based on the deformed version of correspondence, we calculate the pseudoentropy for an entangling surface consisting of two antipodal points on a sphere and find it is exactly dual to the complex geodesic in the bulk.
Paper Structure (3 sections, 36 equations, 3 figures)

This paper contains 3 sections, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Wheeler-DeWitt equation and $T\bar{T}$ flow
  3. Holographic Entanglement Entropy

Figures (3)

  • Figure 1: The $T\bar{T}$-deformed version of the $\text{dS}_{3}$/$\text{CFT}_{2}$ correspondence, with the Lorentzian time $t$ in the global coordinates of the $\text{dS}_{3}$ spacetime.
  • Figure 2: The subsystem $A$ within a non-unitary QFT residing on a two-sphere, with black points indicating the codimension-2 entangling surface.
  • Figure 3: Left panel: Geodesics connecting to the entangling surface in the $\text{dS}_{3}$. The red line denotes one spacelike geodesic and two green lines denote two timelike geodesics. The purple line denotes a spacelike interval $A$ on the two-sphere. Right panel: The entangling surface consists of two antipodal points on the two-sphere.