Abstract
We derive the holographic entanglement entropy functional for a generic gravitational theory whose action contains terms up to cubic order in the Riemann tensor, and in any dimension. This is the simplest case for which the so-called splitting problem manifests itself, and we explicitly show that the two common splittings present in the literature — minimal and non-minimal — produce different functionals. We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4- dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling.
Highlights
Understand more deeply how holography works in theories whose duals are more generic CFTs
We apply our results to the particular examples of a boundary disk and a boundary strip in a state dual to 4dimensional Poincaré AdS in Einsteinian Cubic Gravity, obtaining the bulk entanglement surface for both functionals and finding that causal wedge inclusion is respected for both splittings and a wide range of values of the cubic coupling
After having obtained the entanglement entropy functional using the minimal and non-minimal prescriptions one can turn the question around and ask: if we use these functionals for a cubic theory with a finite coupling, will either of them produce unwanted, unphysical, behaviour? we set out to do just that, we investigate a fundamental property known as causal wedge inclusion
Summary
In a holographic CFT dual to Einstein gravity, the entanglement entropy of a boundary region A is given by the area of an associated codimension-2 surface [25, 26]: S. Notice that Rényi entropies are defined for n ∈ N , an analytic continuation in n is assumed before taking the limit n → 1 All this discussion has been restricted to the field theory, but if this is holographically dual to a gravitational one, it should be possible to find a bulk solution Bn dual to the n-fold cover. In (2.4) we seem to be doing a first order variation away from this solution, so we could naively expect that expression to vanish This is not so because, when varying, we are changing the opening angle at C1 = limn→1 Cn, which as mentioned should be excluded from the action integral and that procedure introduces a boundary where conditions are changing if we vary n. C1 can be characterized as the previously defined surface γA which is homologous to the boundary region A
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