Reflected entropy and timelike entanglement in TT¯ -deformed CFT2…

We develop a covariant formalism to investigate the mixed state entanglement between time-dependent boosted subsystems in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="normal">T</a:mi><a:mover accent="true"><a:mi mathvariant="normal">T</a:mi><a:mo stretchy="false">¯</a:mo></a:mover></a:math>-deformed <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:msub><g:mrow><g:mi>CFT</g:mi></g:mrow><g:mrow><g:mn>2</g:mn></g:mrow></g:msub><g:mi mathvariant="normal">s</g:mi></g:mrow></g:math> through the reflected entropy. To this end we utilize a conformal perturbation theory to obtain the Rényi reflected entropy through the partition function on the replica manifold. The correction to the reflected entropy to the first order in the deformation parameter <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:mi>μ</j:mi></j:math> is then obtained in the replica limit for finite temperature and finite-sized systems. We further perform an analytic continuation of our results to obtain the reflected entropy for timelike subsystems in such <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"><l:mi mathvariant="normal">T</l:mi><l:mover accent="true"><l:mi mathvariant="normal">T</l:mi><l:mo stretchy="false">¯</l:mo></l:mover></l:math>-deformed <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mrow><r:mrow><r:msub><r:mrow><r:mi>CFT</r:mi></r:mrow><r:mrow><r:mn>2</r:mn></r:mrow></r:msub></r:mrow><r:mi mathvariant="normal">s</r:mi></r:mrow></r:math>. We verify our field theoretic computations for both spacelike and timelike subsystems by obtaining the dual EWCS in the corresponding bulk cutoff <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mrow><u:msub><u:mrow><u:mi>AdS</u:mi></u:mrow><u:mrow><u:mn>3</u:mn></u:mrow></u:msub></u:mrow></u:math> geometries and find perfect agreement between the two. Published by the American Physical Society 2024