Entanglement entropy vs. free energy in IIB supergravity duals for 5d SCFTs

TL;DR

The work tests holographic duals for 5d SCFTs in type IIB string theory by computing the finite parts of the free energy on $S^5$ and the entanglement entropy for spherical regions in AdS$_6$-based backgrounds with pole singularities. By deriving and evaluating the on-shell action and the Ryu–Takayanagi minimal surfaces for 3–5 pole configurations, the authors show that the pole singularities are mild and do not contribute finite parts, and that the finite EE matches the finite free-energy quantity, as expected from general QFT arguments. The results provide quantitative confirmation of the proposed AdS/CFT duals, hint at a long-quiver nature of the dual SCFTs, and reveal characteristic $N^4$ scaling and $ ext{Vol}_{S^5}$-dependent structures (including factors of $\zeta(3)$) consistent with localization insights. Overall, the paper strengthens the holographic interpretation of DHoker– collaborators’ IIB solutions and offers concrete data for future field-theory localization and brane-web analyses.

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.

Figures (3)

• Figure 1: The left hand side shows $\theta$ as function of $p_3$, for the 4-pole solution with residues given in eq. (\ref{['eq:4-pole-spin']}). The right hand side shows $I_0$, which via (\ref{['eq:int']}) corresponds to the on-shell action.
• Figure 2: The left hand side shows a 5-brane intersection corresponding to the charges in (\ref{['eqn:5pole-residues']}). On the right hand side is a $\log$-$\log$ plot of $I_0$ for the 5-pole solution with residues given in (\ref{['eqn:5pole-residues']}). Via (\ref{['eq:int']}) this corresponds to the on-shell action, as function of $M/N$. The constant dot-dashed line shows $80\pi\zeta(3)\cdot 16N^4$, which, via (\ref{['eq:3-pole-I0']}), is the value of $I_0$ for the 3-pole solution resulting from (\ref{['eqn:5pole-residues']}) for $M=0$. The dashed line shows $280\pi\zeta(3)\cdot 16M^2N^2$, which, via (\ref{['eq:4-pole']}), is $I_0$ for a 4-pole solution with $-Z_+^1=Z_+^3=2iN$ and $Z_+^2=-Z_+^4=M$.
• Figure 3: Global deformation (in the classification of Aharony:1997juAharony:1997bh) of the brane intersection shown in fig. \ref{['fig:5-pole-a']}, corresponding to a relevant deformation of the dual SCFT.