Abstract
We study entanglement entropy and the free energy in recently constructed holographic duals for 5d SCFTs in type IIB supergravity. The solutions exhibit mild singularities, which could potentially complicate holographic applications. We use the relation of the entanglement entropy for a spherical entangling surface to the free energy of the field theory on the five sphere as a well-motivated benchmark to assess how problematic the singularities are. The holographic supergravity computations give well-defined results for both quantities and they satisfy the expected relations. This supports the interpretation of the solutions as holographic duals for 5d SCFTs and gives first quantitative indications for the nature of the dual SCFTs.
Highlights
Supergravity duals in type IIA supergravity have been known for some time, but they are singular [8, 9]
We study entanglement entropy and the free energy in recently constructed holographic duals for 5d SCFTs in type IIB supergravity
Due to the singularities in the solutions, the holographic computation of the free energy had to proceed through the entanglement entropy of a spherical region, which is less sensitive to the singularities in the geometry
Summary
The type IIB supergravity solutions we consider in this paper have been derived and discussed in detail in [14,15,16], and we will only give a brief review introducing the quantities that will be relevant for the computation of free energy and entanglement entropy. With a complex coordinate w on Σ, the metric and the 2-form field are parametrized by scalar functions f22, f62, ρ2 and C on Σ, ds2 = f62 ds2AdS6 + f22 ds2S2 + 4ρ2dwdw , C(2) = C volS2. The solutions are expressed in terms of two holomorphic functions A± on Σ, which are given by. Regularity of the solutions requires that κ2 and G are both positive in the interior of Σ and vanish on the boundary. These regularity conditions are satisfied if the residues are given by. The explicit form of the functions parametrizing the metric is given by f62. The function C parametrizing the 2-form field is given by
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