Entanglement Entropy and T T ¯ Deformation

We consider the entanglement entropies in dS d sliced (A)dS d+1 in the presence of a hard radial cutoff. By considering a one parameter family of analytic solutions, parametrized by their turning point in the bulk r , we are able to compute the entanglement entropy for generic intervals on the cutoff slice. It has been proposed that the field theory dual of this scenario is a strongly coupled CFT, deformed by a certain irrelevant deformation -the socalled TT deformation. Surprisingly, we find that we may write the entanglement entropies formally in the same way as the entanglement entropy for antipodal points on the sphere by introducing an effective radius R eff = R cos(β ), where R is the radius of the sphere and β related to the length of the interval. Geometrically, this is equivalent to following the TT trajectory until the generic interval corresponds to antipodal points on the sphere. Finally, we check our results by comparing the asymptotic behavior (no Dirichlet wall present) with the results of Casini, Huerta and Myers. In the second part of this work, we extend the field theory calculation of the entanglement entropy for antipodal points for a d-dimensional field theory in context of DS/dS holography.One remarkable development in the recent years has been a novel access to irrelevant (nonrenormalizable) deformations in two dimensional quantum field theories (QFTs). Unlike the usual irrelevant deformations, the so-called TT deformation [1-3] has the intriguing feature that it is -unlike the usual irrelevant deformations -exactly solvable. Starting from a generic seed QFT, we are able to define a trajectory from the IR to the UV in the field theory space triggered by deforming the QFT with a TT deformation in each step. Even through the theory flows towards the UV, we are still able to derive a lot of interesting quantities in exact form simply from possessing an understanding of undeformed theory. These quantities include the finite volume spectrum, the S-matrix and the deformed classical Lagrangian -all of which have been extensively discussed in the literature (see [38] for lecture notes).An interesting approach to TT deformations is the proposal of a holographic dual by McGough, Mezei, and Verlinde [4] in order to use the powerful toolkit provided by holographic dualities for studying problems in strongly coupled field theories. From a bulk perspective, deforming a field theory by an irrelevant deformation has drastic effects on the UV behavior. McGough, Mezei, and Verlinde conjectured to simply chop off the asymptotic region of the spacetime. In other words, deforming the conformal field theory (CFT) by the TT operator is dual to introducing a hard radial cutoff (Dirichlet wall) at a finite radial position r = r c in the bulk. The hard radial cutoff removes the UV region of the spacetime and the dual field theory which lives on the cutoff surface is no longer conformal. For Anti-de Sitter (AdS) this was more extensively studied in [11].One interesting aspect of quantum theories -especially with re...

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Section: Sphere Partition Functions and Entanglement Entropymentioning

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See 3 more Smart Citations

Entanglement entropy and $$ T\overline{T} $$ deformations beyond antipodal points from holography

Grieninger

2019

Modular covariance and uniqueness of $$ J\overline{T} $$ deformed CFTs

Aharony

Datta

Giveon

et al. 2019

We study families of two dimensional quantum field theories, labeled by a dimensionful parameter µ, that contain a holomorphic conserved U(1) current J(z). We assume that these theories can be consistently defined on a torus, so their partition sum, with a chemical potential for the charge that couples to J, is modular covariant. We further require that in these theories, the energy of a state at finite µ is a function only of µ, and of the energy, momentum and charge of the corresponding state at µ = 0, where the theory becomes conformal. We show that under these conditions, the torus partition sum of the theory at µ = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in µ, to be that of a µJT deformed conformal field theory (CFT). We derive a flow equation for the JT deformed partition sum, and use it to study non-perturbative effects. We find non-perturbative ambiguities for any non-zero value of µ, and comment on their possible relations to holography.

Modular invariance and uniqueness of $$ T\overline{T} $$ deformed CFT

Aharony

Datta

Giveon

et al. 2019

166

205

Any two dimensional quantum field theory that can be consistently defined on a torus is invariant under modular transformations. In this paper we study families of quantum field theories labeled by a dimensionful parameter t, that have the additional property that the energy of a state at finite t is a function only of t and of the energy and momentum of the corresponding state at t = 0, where the theory becomes conformal. We show that under this requirement, the partition sum of the theory at t = 0 uniquely determines the partition sum (and thus the spectrum) of the perturbed theory, to all orders in t, to be that of a TT deformed CFT. Non-perturbatively, we find that for one sign of t (for which the energies are real) the partition sum is uniquely determined, while for the other sign we find non-perturbative ambiguities. We characterize these ambiguities and comment on their possible relations to holography.