Abstract Recently, it was proposed that a
TT T T ¯ deformed CFT is dual to a gravity theory in an asymptotically AdS spacetime at finite radial cutoff. Motivated by this proposal, we explore some aspects of Hyperscaling Violating geometries at finite cutoff and zero temperature. We study holographic entanglement entropy, mutual information (HMI) and entanglement wedge cross section (EWCS) for entangling regions in the shape of strips. It is observed that the HMI shows interesting features in comparison to the very small cutoff case: it is a decreasing function of the cutoff. It is finite when the distance between the two entangling regions goes to zero. The location of its phase transition also depends on the cutoff, and decreases by increasing the cutoff. On the other hand, the EWCS is a decreasing function of the cutoff. It does not show a discontinuous phase transition when the HMI undergoes a first-order phase transition. However, its concavity changes. Moreover, it is finite when the distance between the two strips goes to zero. Furthermore, it satisfies the bound EW ≥
2I I 2 for all values of the cutoff.
We study the entanglement entropy (EE) and the R\'enyi entropy (RE) of multiple intervals in two-dimensional
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 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.
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.
The quantum entanglement measures for
TT deformed field theory on boundary, deformation coefficient
μ, with dual bulk geometry with finite radial cutoff
ρc, for entangling region is single or disjoint intervals on the boundary, of length l is expected to give global description of these measures over the complete parameter-regime of
(l,μ) or on 2D
(l,ρc) plane, because it is solvable irrelevant deformation. Here, to find quantum-measures through RT prescription, from Hyperscaling violating bulk geometry with finite radial cut off, we found mathematically it is impossible, to obtain such global form, since the turning point
ρ0(l,ρc), neither in its exact or in any perturbative form, is solvable globally, can describe these quantum measures at most locally over some specific regime in 2D
(l,ρc) plane! However, to find such global form, we found, on application of RT formalism, a global symmetry structure, from the considered geometry emerges, over 2D parameter-space, irrespective of d,
θ, which alongwith global b.c and other consistency conditions, fix
ρ0(l,ρc) globally, exactly in $l >> ρ_c $ and
ρc>>l regime and as some interpolating expressions, very close to the exact one in other regime. Some of the quantum entanglement measures with this
ρ0(l,ρc), with our intuitively predicted behaviour for them in the deformed theory, derived and shown, behaving accordingly. The impact of this emergent symmetry on these quantum-measures is discussed, the possible space time origin of this symmetry is explored, although the later aspect is subjected to a proper and detailed study.
Abstract We consider the entanglement entropies in dSd sliced (A)dSd+1 in the presence of a hard radial cutoff for 2 ≤ d ≤ 6. By considering a one parameter family of analytical 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 so-called
TT T T ¯ 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 Reff = R cos(βϵ), where R is the radius of the sphere and βϵ related to the length of the interval. Geometrically, this is equivalent to following the
TT T T ¯ 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. We then switch on counterterms on the cutoff slice which are important with regards to the field theory calculation. We explicitly compute the contributions of the counterterms to the entanglement entropy by considering the Wald entropy. 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. We find excellent agreement with the results from holography and show, in particular, that the effects of the counterterms in the field theory calculation match the Wald entropy associated with the counterterms on the gravity side.