Distributional Geometry of Squashed Cones

By D. Fursaev, A. Patrushev, S. Solodukhin. 2013

185 citations recorded by the source corpus.

A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational O(2) symmetry in a subspace orthogonal to a singular surface $\Sigma$ so that the surface is allowed to have extrinsic curvatures. A new feature of the squashed conical singularities is that the surface terms in the integral invariants, in the limit of small angle deficit, now depend also on the extrinsic curvatures of $\Sigma$. A case of invariants which are quadratic polynomials of the Riemann curvature is elaborated in different dimensions and applied to several problems related to entanglement entropy. The results are in complete agreement with computations of the logarithmic terms in entanglement entropy of 4D conformal theories [2]. Among other applications of the suggested method are logarithmic terms in entanglement entropy of non-conformal theories and a holographic formula for entanglement entropy in theories with gravity duals.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/2c9dba8fb237ee02d030390aacc53df42f4fe312

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Citations in the corpus

Quantum extremal surfaces: holographic entanglement entropy beyond the classical regime (2014, background): “8The entropy formulae in more restricted cases are given by [31, 36, 37, 38, 39].”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “Here LA denotes a particular local operator in the bulk integrated over γA: at leading order in Newton’s constant G we have LA = Area(γA) 4G , while at higher orders, both in G but also in other couplings such as α′, there are corrections to LA involving various intrisic and extrinsic quantities int”
Geometric entropy and edge modes of the electromagnetic field (2015, background): “This would allow us to determine the dependence of the entanglement entropy on the extrinsic geometry of the entangling surface, to compare to [42, 55].”