The Gravity Dual of Supersymmetric Renyi Entropy

Supersymmetric Renyi entropies are defined for three-dimensional N=2 superconformal field theories on a branched covering of a three-sphere by using the localized partition functions. Under a conformal transformation, the branched covering is mapped to S^1 x H^2, whose gravity dual is the charged topological AdS_4 black hole. The black hole can be embedded into four-dimensional N=2 gauged supergravity where the mass and charge are related so that it preserves half of the supersymmetries. We compute the supersymmetric Renyi entropies with and without a certain type of Wilson loop operators in the gravity theory. We find they agree with those of the dual field theories in the large-N limit.Comment: 13 pages, 2 figures; v2: typos correcte

Free Yang-Mills vs. Toric Sasaki-Einstein

It has been known that the Bekenstein-Hawking entropy of the black hole in AdS_5 * S^5 agrees with the free N=4 super Yang-Mills entropy up to the famous factor 4/3. This factor can be interpreted as the ratio of the entropy of the free Yang-Mills to the entropy of the strongly coupled Yang-Mills. In this paper we compute this factor for infinitely many N=1 SCFTs which are dual to toric Sasaki-Einstein manifolds. We observed that this ratio always takes values within a narrow range around 4/3. We also present explicit values of volumes and central charges for new classes of toric Sasaki-Einstein manifolds.Comment: 18 pages, 7 figures, latex, comments and a reference added (v2), explanation improved and references added (v3), a reference added (v4

Supersymmetric Renyi Entropy

We consider 3d N>= 2 superconformal field theories on a branched covering of a three-sphere. The Renyi entropy of a CFT is given by the partition function on this space, but conical singularities break the supersymmetry preserved in the bulk. We turn on a compensating R-symmetry gauge field and compute the partition function using localization. We define a supersymmetric observable, called the super Renyi entropy, parametrized by a real number q. We show that the super Renyi entropy is duality invariant and reduces to entanglement entropy in the q -> 1 limit. We provide some examples.Comment: 39 pages, 4 figure

A Holographic Proof of R\'enyi Entropic Inequalities

We prove R\'enyi entropic inequalities in a holographic setup based on the recent proposal for the holographic formula of R\'enyi entropies when the bulk is stable against any perturbation. Regarding the R\'enyi parameter as an inverse temperature, we reformulate the entropies in analogy with statistical mechanics, which provides us a concise interpretation of the inequalities as the positivities of entropy, energy and heat capacity. This analogy also makes clear a thermodynamic structure in deriving the holographic formula. As a by-product of the proof we obtain a holographic formula to calculate the quantum fluctuation of the modular Hamiltonian. A few examples of the capacity of entanglement are examined in detail.Comment: 29 pages, 1 figure; v3: references added, our assumption for the proof clarifie

Entanglement Entropy of Annulus in Three Dimensions

The entanglement entropy of an annulus is examined in a three-dimensional system with or without a gap. For a free massive scalar field theory, we numerically calculate the mutual information across an annulus. We also study the holographic mutual information in the CGLP background describing a gapped field theory. We discover four types of solutions as the minimal surfaces for the annulus and classify the phase diagrams by varying the inner and outer radii. In both cases, we find the mutual information satisfies the monotonicity dictated by the unitarity and decays exponentially fast as the gap scale is increased. We speculate this is a universal behavior in any gapped system.Comment: 29 pages, 13 figures, v2: references added, minor change