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 Toverline{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 Toverline{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.
Highlights
An interesting approach to T Tdeformations 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
This hard radial cutoff chops off the asymptotic UV region of the gravitational theory which is proposed to be the holographic dual to a conformal field theory (CFT) deformed by the irrelevant T Toperator
This corresponds to the scenario where we follow the T Ttrajectory until the points of the generic interval are antipodal on a sphere with radius Reff
Summary
Ds2 = dr2 + (L sin(h)(r/L))2 − cos2(β) dτ 2 + dβ2 + sin2(β) dΩ2D−3. In these coordinates, the horizon is located at r = 0, the AdS boundary at r = ∞ and the dS central slice at r/L = π/2. We want to calculate entanglement entropies associated with spherical entangling surfaces centered around the center of the static patch for an observer located at τ =0 β = β0 ∈ [0, π/2]. According to the Ryu-Takayanagi formula, our task at hand is to calculate the surface minimizing the area. We will do this by committing to a parametrization and determining the entangling surfaces by solving the Euler-Lagrange equations
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