Abstract
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds. We consider singular surfaces consisting of cones or creases in diverse dimensions. The structure of UV divergences of entanglement entropy exhibits new logarithmic terms whose coefficients, being cut-off independent, could be used to define new central charges in the nearly smooth limit. We also show that there is a relation between these central charges and the one appearing in the two-point function of the energy-momentum tensor. Finally we examine how this relation is affected by considering higher-curvature terms in the gravitational action.
Highlights
It directly related to the cut-off independent terms of the entanglement entropy computed for a smooth entangling region
We study the holographic entanglement entropy for singular surfaces in theories described holographically by hyperscaling violating backgrounds
ΩnVd−n−2Ld rFθ π dφ sinn φ ρn+1 1 + ρ 2 dr rdθ. Using this expression and following the procedure we have explored in the previous section one can find the divergent terms of holographic entanglement entropy for the smooth entangling surface (3.2) as follows i=0 dθ b2i
Summary
We shall study holographic entanglement entropy on a singular region consisting of an n dimensional cone cn. The divergent terms of the holographic entanglement entropy for dθ = n + 2 are From this general expression we observe that the holographic entanglement entropy for a singular surface shaped as cn ×Rd−n−2 contains many divergent terms including, when dθ is an odd number, a logarithmically divergent term whose coefficient is universal, in the sense that it is ε independent. This is the same behaviour for a generic entangling region where in even dimensional CFTs the entanglement entropy contains always a logarithmically divergent term.
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