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arXiv:2307.04832 · Physical review. D/Physical review. D.

Odd entanglement entropy in TT¯ deformed CFT2s and holography

Debarshi Basu, Saikat Biswas, Ankur Dey, Boudhayan Paul, Gautam Sengupta

Published Dec 15, 2023• 8 citations
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Abstract

We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in $\mathrm{T}\overline{\mathrm{T}}$ deformed ${\mathrm{CFT}}_{2}\mathrm{s}$. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in $\mathrm{T}\overline{\mathrm{T}}$ deformed thermal ${\mathrm{CFT}}_{2}\mathrm{s}$ in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Ba\~nados-Teitelboim-Zanelli geometries. We further show that for finite size $\mathrm{T}\overline{\mathrm{T}}$ deformed ${\mathrm{CFT}}_{2}\mathrm{s}$ at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.

DOI
10.1103/physrevd.108.126013

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We construct a replica technique to perturbatively compute the odd entanglement entropy (OEE) for bipartite mixed states in TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s. This framework is then utilized to obtain the leading-order correction to the OEE for two disjoint intervals, two adjacent intervals, and a single interval in TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed thermal CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s in the large central charge limit. The field theory results are subsequently reproduced in the high-temperature limit from holographic computations for the entanglement wedge cross sections in the dual bulk finite cutoff Ba~nados-Teitelboim-Zanelli geometries. We further show that for finite size TT‾\mathrm{T}\overline{\mathrm{T}}TT deformed CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s at zero temperature the corrections to the OEE are vanishing to the leading order from both field theory and bulk holographic computations.
We apply a suitable replica technique to develop a perturbative expression for the entanglement negativity of bipartite mixed states in TT‾\mathrm{T}\overline{\mathrm{T}}TT-deformed CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s up to the first order in the deformation parameter. Utilizing our perturbative construction we compute the entanglement negativity for various bipartite mixed states involving two disjoint intervals, two adjacent intervals, and a single interval in a TT‾\mathrm{T}\overline{\mathrm{T}}TT-deformed CFT2{\mathrm{CFT}}_{2}CFT2​ at a finite temperature, in the large central-charge limit. Subsequently, we advance appropriate holographic constructions to compute the entanglement negativity for such bipartite states in TT‾\mathrm{T}\overline{\mathrm{T}}TT-deformed thermal CFT2s{\mathrm{CFT}}_{2}\mathrm{s}CFT2​s dual to BTZ black holes in a finite cutoff bulk geometry and find agreement with the corresponding field theoretic results in the limit of small deformation parameter.
Abstract We obtain the odd entanglement entropy (OEE) for bipartite mixed states in ( 1 + 1 ) -dimensional boundary conformal field theories (BCFT 2 s) utilizing an appropriate replica technique. For the generic configuration of two disjoint intervals, the large- c factorization of the twist field correlator leads to several distinct phases depending on the relative sizes and separations of the intervals. The resulting expressions match consistently with the entanglement wedge cross section (EWCS) for the bulk AdS 3 braneworld geometries, thereby extending the proposed holographic duality between the difference of the OEE and the entanglement entropy with the EWCS to BCFT setups. Furthermore, we obtain the OEE for these mixed states in related holographic moving mirror models which simulate Hawking radiation from black holes and verify the above duality in these time-dependent backgrounds. In this context we analyze the time evolution of the OEE and establish the analogues of Page curves for this mixed-state correlation measure.
Abstract The odd entanglement entropy (OEE) for bipartite states in a class of (1+1)(1+1)(1+1) ( 1 + 1 ) -dimensional Galilean conformal field theories ( GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 ) is obtained through an appropriate replica technique. In this context our results are compared with the entanglement wedge cross section (EWCS) for (2+1)(2+1)(2+1) ( 2 + 1 ) -dimensional asymptotically flat geometries dual to the GCFT1+1GCFT_{1+1}GCFT1+1​ G C F T 1 + 1 in the framework of flat holography. We find that our results are consistent with the duality of the difference between the odd entanglement entropy and the entanglement entropy of bipartite states, with the bulk EWCS for flat holographic scenarios.
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In this paper, we study the entanglement entropy of a single interval on a cylinder in two-dimensional TT‾T\overline{T}TT-deformed conformal field theory (CFT). 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 ccc CFT, which is proposed to be dual to a AdS3{\mathrm{AdS}}_{3}AdS3​ 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.
We define a new information theoretic quantity called odd entanglement entropy (OEE) which enables us to compute the entanglement wedge cross section in holographic conformal field theories (CFTs). The entanglement wedge cross section has been introduced as a minimal cross section of the entanglement wedge, a natural generalization of the Ryu-Takayanagi surface. By using the replica trick, we explicitly compute the OEE for two-dimensional holographic CFT (three-dimensional anti-de Sitter space and planar Bañados-Teitelboim-Zanelli black hole) and see agreement with the entanglement wedge cross section. We conjecture this relation will hold in general dimensions.