Abstract
In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional $T\overline{T}$-deformed conformal field theory. For such case, the (R\'enyi) entanglement entropy takes a universal form in a CFT. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of the conformal perturbation theory. We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case. For the deformed holographic large $c$ CFT, which is proposed to be dual to a AdS$_3$ gravity in a finite region, we find the agreement with the holographic entanglement entropy via the Ryu-Takayanagi formula. Moreover, we compute the leading order correction to the R\'enyi entropy, and discuss its holographic picture as well.
Highlights
The integrable quantum field theory allows us to understand the nonperturbative aspects of the quantum field theory
We find that the correction to the entanglement entropy is nonvanishing in the finite temperature case, while it is vanishing in the finite size case
For the deformed holographic large c conformal field theory (CFT), which is proposed to be dual to a AdS3 gravity in a finite region, we find the agreement with the holographic entanglement entropy via the Ryu-Takayanagi formula
Summary
The integrable quantum field theory allows us to understand the nonperturbative aspects of the quantum field theory. The TT -deformation opens a new window to study the AdS=CFT correspondence. We would like to study the entanglement entropy in the TT -deformed conformal field theory. In particular we pay special attention to the entanglement entropy in the deformed holographic CFT and investigate its implication in the AdS=CFT correspondence. We show that for the AdS3 gravity with a cutoff surface, the on-shell action includes a cutoff-dependent term, which corresponds to the leading order correction due to the TT -deformation in the partition function in the CFT. The authors in [26] considered the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere
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