Universal entanglement for higher dimensional cones

Abstract

The entanglement entropy of a generic $d$-dimensional conformal field theory receives a regulator independent contribution when the entangling region contains a (hyper)conical singularity of opening angle $\Omega$, codified in a function $a^{(d)}(\Omega )$. In arXiv:1505.04804, we proposed that for three-dimensional conformal field theories, the coefficient $\sigma$ characterizing the smooth surface limit of such contribution ($\Omega \to \pi$) equals the stress tensor two-point function charge $C_T$, up to a universal constant. In this paper, we prove this relation for general three-dimensional holographic theories, and extend the result to general dimensions. In particular, we show that a generalized coefficient ${\sigma }^{(d)}$ can be defined for (hyper)conical entangling regions in the almost smooth surface limit, and that this coefficient is universally related to $C_T$ for general holographic theories, providing a general formula for the ratio ${\sigma }^{(d)}/C_T$ in arbitrary dimensions. We conjecture that the latter ratio is universal for general CFTs. Further, based on our recent results in arXiv:1507.06997, we propose an extension of this relation to general Rényi entropies, which we show passes several consistency checks in $d=4$ and $d=6$.

22 pages, 3 figures, 2 tables; v3: minor modifications to match published version, references added

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Cited by in corpus (26)

• The Gravity Dual of Renyi Entropy
• Rényi entropy and conformal defects
• Aspects of capacity of entanglement
• Holographic Complexity for Defects Distinguishes Action from Volume
• Shape Dependence of Holographic Rényi Entropy in General Dimensions
• Superconformal surfaces in four dimensions
• Shape Dependence of Holographic Renyi Entropy in Conformal Field Theories
• Bounds on corner entanglement in quantum critical states
• Holographic Subregion Complexity for Singular Surfaces
• Comments on Squashed-sphere Partition Functions
• Holographic Mutual Information for Singular Surfaces
• Surface operators in the 6d $\mathcal{N}=(2,0)$ theory
• Entanglement Entropy in Generalised Quantum Lifshitz Models
• Corner contributions to holographic entanglement entropy in non-conformal backgrounds
• Gravitational dual of the Rényi twist displacement operator
• Shape dependence of renormalized holographic entanglement entropy
• Cubic trihedral corner entanglement for a free scalar
• On the logarithmic divergent part of entanglement entropy, smooth versus singular regions
• Generalized Gravitational Entropy from Total Derivative Action
• Shape dependence of two-cylinder Renyi entropies for free bosons on a lattice
• Entanglement entropy and localization in disordered quantum chains
• A holographic proof of the universality of corner entanglement for CFTs
• Conical defects and holography in topological AdS gravity
• Universal corner contributions to entanglement negativity
• Holographic entanglement entropy for hollow cones and banana shaped regions
• Universal divergence of the Renyi entropy of a thinly sliced torus at the Ising fixed point