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We calculate the shape dependence of entanglement entropy in(5+1)-dimensional conformal field theory in terms of the extrinsic curvature ofthe entangling surface, the opening angles of possible conical singularities,and the conformal anomaly coefficients, which are required to obey a singleconstraint. An important special case of this result is given by theinteracting (2,0) theory describing a large number of coincident M5-branes. Toderive the more general result we rely crucially on the holographicprescription for calculating entanglement entropy using Lovelock gravity. Wetest the conjecture by relating the entanglement entropy of the free massless(1,0) hypermultiplet in (5+1)-dimensions to the entanglement entropy of thefree massive chiral multiplet in (2+1)-dimensions, which we calculatenumerically using lattice techniques. We also present a numerical calculationof the (2+1)-dimensional renormalized entanglement entropy for the free massiveDirac fermion, which is shown to be consistent with the F-theorem.

Exact and Numerical Results on Entanglement Entropy in (5+1)-Dimensional CFT