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.