Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1911.04618 · Nuclear Physics B

Entropic c–functions in TT‾,JT‾,TJ‾ deformations

Meseret Asrat

Published Sep 21, 2020• 14 citations
arXivHTMLPDF

Abstract

We study the holographic entanglement entropy of an interval in a quantum field theory obtained by deforming a holographic two–dimensional conformal field theory via a general linear combination of irrelevant operators that are closely related to, but nonetheless distinct from, TT‾, JT‾ and TJ‾, and compute the Casin–Huerta entropic c–function. In the ultraviolet, for a particular combination of the deformation parameters, we find that the leading order dependence of the entanglement entropy on the length of the interval is given by a square root but not logarithmic term. Such power law dependence of the entanglement entropy on the interval length is quite peculiar and interesting. We also find that the entropic c–function is ultraviolet regulator independent, and along the renormalization group upflow towards the ultraviolet, it is non–decreasing. We show that in the ultraviolet the entropic c–function exhibits a power law divergence as the interval length approaches a minimum finite value determined in terms of the deformation parameters. This value sets the non–locality scale of the theory.

DOI
10.1016/j.nuclphysb.2020.115186

Related papers

Entanglement entropy in TT¯ -deformed CFT

Bin Chen, Lin Chen, Peng-Xiang Hao

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 (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 $c$ CFT, which is proposed to be dual to a ${\mathrm{AdS}}_{3}$ 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.

arXiv:1807.08293•Physical review. D/Physical review. D.•Oct 29, 2018•96 citations

Entanglement and Rényi entropy of multiple intervals in TT¯ -deformed CFT and holography

Hyun-Sik Jeong, Keun-young Kim A, Mitsuhiro Nishida

We study the entanglement entropy (EE) and the R\'enyi entropy (RE) of multiple intervals in two-dimensional $T\overline{T}$- deformed conformal field theory (CFT) at a finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a nontrivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cutoff radius (dual to the $T\overline{T}$ deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected ($s$-channel) and connected ($t$-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.

arXiv:1906.03894•Physical review. D/Physical review. D.•Nov 26, 2019•57 citations

Entanglement Entropy and TT¯ Deformation

William Donnelly, Vasudev Shyam

Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough et al. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the TT[over ¯] deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the TT[over ¯]-deformed CFT is the holographic dual of a finite region of spacetime.

arXiv:1806.07444•Physical Review Letters•Sep 26, 2018•145 citations

Entanglement entropy of singular surfaces under relevant deformations in holography

Mostafa Ghasemi, Shahrokh Parvizi

In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.

arXiv:1709.08169•Journal of High Energy Physics•Feb 1, 2018•8 citations

On holographic entanglement density

Nikola I. Gushterov, Andy O’Bannon, Ronnie Rodgers

We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.

arXiv:1708.09376•Journal of High Energy Physics•Oct 1, 2017•13 citations

Correlation functions, entanglement and chaos in the TT¯ / JT¯ -deformed CFTs

Song He, Hongfei Shu

In this paper, we regard the $T\\bar{T}$/$J\\bar{T}$-deformed CFTs as perturbation theories and compute the first order correction of the correlation functions due to the $T\\bar{T}$/$J\\bar{T}$-deformation. As applications, we study the R\\'enyi entanglement entropy of excited state in the $T\\bar{T}$/$J\\bar{T}$-deformed two-dimensional CFTs. We find, up to the perturbation first order of the deformation, the R\\'enyi entanglement entropy of locally excited state will obtain a nontrivial time dependence. The excess of the R\\'enyi entanglement entropy of locally excited state will also be dramatically changed up to order ${\\cal O}(c)$. Furthermore, we investigate the out of time ordered correlation function to confirm that the $T\\bar{T}$/$J\\bar{T}$-deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.

•Jan 1, 2020•75 citations
We study the holographic entanglement entropy of an interval in a quantum field theory obtained by deforming a holographic two–dimensional conformal field theory via a general linear combination of irrelevant operators that are closely related to, but nonetheless distinct from, TT‾, JT‾ and TJ‾, and compute the Casin–Huerta entropic c–function. In the ultraviolet, for a particular combination of the deformation parameters, we find that the leading order dependence of the entanglement entropy on the length of the interval is given by a square root but not logarithmic term. Such power law dependence of the entanglement entropy on the interval length is quite peculiar and interesting. We also find that the entropic c–function is ultraviolet regulator independent, and along the renormalization group upflow towards the ultraviolet, it is non–decreasing. We show that in the ultraviolet the entropic c–function exhibits a power law divergence as the interval length approaches a minimum finite value determined in terms of the deformation parameters. This value sets the non–locality scale of the theory.
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 study the entanglement entropy (EE) and the R\'enyi entropy (RE) of multiple intervals in two-dimensional TT‾T\overline{T}TT- deformed conformal field theory (CFT) at a finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a nontrivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cutoff radius (dual to the TT‾T\overline{T}TT deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected (sss-channel) and connected (ttt-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.
Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough et al. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the TT[over ¯] deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the TT[over ¯]-deformed CFT is the holographic dual of a finite region of spacetime.
In the vacuum state of a CFT, the entanglement entropy of singular surfaces contains a logarithmic universal term which is only due to the singularity of the entangling surface. We consider the relevant perturbation of a three dimensional CFT for singular entangling surface. We observe that in addition to the universal term due to the entangling surface, there is a new logarithmic term which corresponds to a relevant perturbation of the conformal field theory with a coefficient depending on the scaling dimension of the relevant operator. We also find a new power law divergence in the holographic entanglement entropy. In addition, we study the effect of a relevant perturbation in the Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic term shows up. This new term is proportional to both the dimension of the relevant operator and the Gauss-Bonnet coupling. We also introduce the renormalized entanglement entropy for a kink region which in the UV limit reduces to a universal positive finite term.
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.
In this paper, we regard the TbarTT\\bar{T}TbarT/JbarTJ\\bar{T}JbarT-deformed CFTs as perturbation theories and compute the first order correction of the correlation functions due to the TbarTT\\bar{T}TbarT/JbarTJ\\bar{T}JbarT-deformation. As applications, we study the R\\'enyi entanglement entropy of excited state in the TbarTT\\bar{T}TbarT/JbarTJ\\bar{T}JbarT-deformed two-dimensional CFTs. We find, up to the perturbation first order of the deformation, the R\\'enyi entanglement entropy of locally excited state will obtain a nontrivial time dependence. The excess of the R\\'enyi entanglement entropy of locally excited state will also be dramatically changed up to order calO(c){\\cal O}(c)calO(c). Furthermore, we investigate the out of time ordered correlation function to confirm that the TbarTT\\bar{T}TbarT/JbarTJ\\bar{T}JbarT-deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.