Entanglement in $\text{T}\bar{\text{T}}$ and root-$\text{T}\bar{\text{T}}$ deformed AdS$_3$/CFT$_2$

TL;DR

The paper analyzes how solvable irrelevant deformations, $T\bar{T}$ and root-$T\bar{T}$, modify entanglement and information-theoretic measures in AdS$_3$/CFT$_2$. Using mixed boundary conditions, it verifies that the entanglement wedge cross section correctly captures reflected entropy for mixed states in $T\bar{T}$-deformed backgrounds and computes first-order corrections to EWCS for BTZ geometries. It further develops root-$T\bar{T}$ deformations, deriving boundary data flows and evaluating holographic and field-theory entanglement entropies for thermal and charged CFT$_2$, including finite-temperature and conserved-charge effects, and discusses QNEC in these deformed theories. The results show consistency between the mixed boundary condition framework and standard AdS/cutoff prescriptions, and reveal new features such as real timelike EE windows and asymmetries in QNEC under boosts. Overall, the work provides a coherent holographic picture of how these deformations affect pure and mixed-state entanglement, with implications for quantum gravity and holographic information theory.

Abstract

In this work, we investigate the effects of $\text{T}\bar{\text{T}}$ and root-$\text{T}\bar{\text{T}}$ deformations on reflected and entanglement entropy in the context of both pure and mixed state entanglement measures. Utilizing a mixed boundary condition framework, we analyze how these deformations modify entanglement structures and explore their implications in three-dimensional AdS space. Our results provide insights into the interplay between solvable irrelevant deformations and quantum information-theoretic quantities, shedding light on the entanglement structure of deformed theories.

Figures (4)

• Figure 1: $\beta=1,~\Omega=0.4,~c=12\pi,~u_c=0.01$
• Figure 2: Left: Variation of the real part of HEE (blue) and $\mathcal{Q}_{\pm}$ (orange) with deformation parameter for a purely timelike interval at $t=2,~\beta=\sqrt{8}\pi,~\Omega=0,~c=12\pi,~u_c=0.01$. Right: Variation of $\mathcal{Q}_{+}$ (orange) and $\mathcal{Q}_{-}$ (green) with deformation parameter for non-vanishing chemical potential at $t=2,~\beta=1,~\Omega=0.4,~c=12\pi,~u_c=0.01$.
• Figure 3: Left panel $t=2,\beta=\sqrt{8}\pi,\Omega=0,c=12\pi, u_c=0.01$, Right panel $t=2,\beta=\sqrt{8}\pi,\Omega=0,c=12\pi, u_c=0.01$
• Figure 4: Left panel $l=2,\beta=1,\Omega=0.4,c=12\pi, u_c=0.01$, Right panel $t=2,\beta=1,\Omega=0.4,c=12\pi, u_c=0.01$