Entanglement entropy for $$ \mathrm{T}\overline{\mathrm{T}} $$, $$ \mathrm{J}\overline{\mathrm{T}} $$, $$ \mathrm{T}\overline{\mathrm{J}} $$ deformed holographic CFT
Abstract We derive the geodesic equation for determining the Ryu-Takayanagi surface in AdS3 deformed by single trace $$ \mu T\overline{T} $$ μT T ¯ + $$ {\varepsilon}_{+}J\overline{T} $$ ε + J T ¯ + $$ {\varepsilon}_{-}T\overline{J} $$ ε − T J ¯ deformation for generic values of (μ, ε+, ε−) for which the background is free of singularities. For generic values of ε±, Lorentz invariance is broken, and the Ryu-Takayanagi surface embeds non-trivially in time as well as spatial coordinates. We solve the geodesic equation and characterize the UV and IR behavior of the entanglement entropy and the Casini-Huerta c-function. We comment on various features of these observables in the (μ, ε+, ε−) parameter space. We discuss the matching at leading order in small (μ, ε+, ε−) expansion of the entanglement entropy between the single trace deformed holographic system and a class of double trace deformed theories where a strictly field theoretic analysis is possible. We also comment on expectation value of a large rectangular Wilson loop-like observable.