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Authors
Toshihiro Ota
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We study two-interval holographic entanglement entropy and entanglement wedge cross section in cutoff AdS. In particular, we investigate phase transitions of them. For two-interval entanglement entropy, the transition point monotonically decreases with a deformation parameter, which means that by the TT deformation the degrees of freedom in subsystems are decreasing. This implies that the effect of the TT deformation can be regarded as the rescaling of the energy scale. We also study entanglement wedge cross section in cutoff AdS, and our result implies that for the entanglement of purification in the TT deformed CFTs phase transition could occur even for fixed subsystems.
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We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be reinterpreted as the rescaling of the energy scale, similar to the $T bar{T}$ deformation. Under the boost and $T bar{T}$ deformation, the $c$-function of the entanglement entropy exactly shows the features expected by the Zamoldchikovs $c$-theorem. The deformed theory is always stationary at a UV fixed point and monotonically flows to another CFT in the IR fixed point. We also show that the holographic entanglement entropy in a Poincare cutoff AdS space can reproduce the exact same result of the $T bar{T}$ deformed theory on a two-dimensional sphere.
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