Entanglement negativity in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> <mml:mover accent="true"> <mml:mrow> <mml:mi mathvariant="normal">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo stretchy="false">¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> -deformed <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>CFT</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:mi mathvariant="normal">s</mml:mi> </mml:mrow> </mml:math>
Debarshi Basu, Lavish Chawla, Boudhayan Paul
Abstract
We apply a suitable replica technique to develop a perturbative expression for the entanglement negativity of bipartite mixed states in $\mathrm{T}\overline{\mathrm{T}}$-deformed ${\mathrm{CFT}}_{2}\mathrm{s}$ up to the first order in the deformation parameter. Utilizing our perturbative construction we compute the entanglement negativity for various bipartite mixed states involving two disjoint intervals, two adjacent intervals, and a single interval in a $\mathrm{T}\overline{\mathrm{T}}$-deformed ${\mathrm{CFT}}_{2}$ at a finite temperature, in the large central-charge limit. Subsequently, we advance appropriate holographic constructions to compute the entanglement negativity for such bipartite states in $\mathrm{T}\overline{\mathrm{T}}$-deformed thermal ${\mathrm{CFT}}_{2}\mathrm{s}$ dual to BTZ black holes in a finite cutoff bulk geometry and find agreement with the corresponding field theoretic results in the limit of small deformation parameter.