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Exact results for five-dimensional superconformal field theories with gravity duals

Daniel L. Jafferis, Silviu S. Pufu

TL;DR

The paper applies supersymmetric localization to compute the exact $S^5$ partition functions of large $N$ five-dimensional SCFTs with $AdS_6$ gravity duals. Localization is performed in IR YM–matter deformations and the resulting free energy is matched to a holographic entanglement-entropy computation in the AdS$_6$ background, reproducing the $F \sim - c N^{5/2}$ scaling. For USp(2N) theories and $Z_n$ orbifolds, explicit large-$N$ saddle densities yield closed forms $F \approx - (9 \sqrt{2} \pi /5) N^{5/2} / \sqrt{8-N_f}$ and $F \approx - (9 \sqrt{2} \pi n^{3/2} N^{5/2}) / (5 \sqrt{8-N_f})$, respectively. The gravity analysis confirms the field-theory results by computing the entanglement entropy across a 3-sphere in the $AdS_6$ background, aligning the universal part with the field-theory $S^5$ free energy and reinforcing the holographic picture for five-dimensional SCFTs.

Abstract

We apply the technique of supersymmetric localization to exactly compute the $S^5$ partition function of several large $N$ superconformal field theories in five dimensions that have $AdS_6$ duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the $S^5$ free energy to a holographic computation of entanglement entropy in the $AdS_6$ duals and find perfect agreement. In particular, we reproduce the $N^{5/2}$ scaling of the $S^5$ free energy that was expected from supergravity.

Exact results for five-dimensional superconformal field theories with gravity duals

TL;DR

The paper applies supersymmetric localization to compute the exact partition functions of large five-dimensional SCFTs with gravity duals. Localization is performed in IR YM–matter deformations and the resulting free energy is matched to a holographic entanglement-entropy computation in the AdS background, reproducing the scaling. For USp(2N) theories and orbifolds, explicit large- saddle densities yield closed forms and , respectively. The gravity analysis confirms the field-theory results by computing the entanglement entropy across a 3-sphere in the background, aligning the universal part with the field-theory free energy and reinforcing the holographic picture for five-dimensional SCFTs.

Abstract

We apply the technique of supersymmetric localization to exactly compute the partition function of several large superconformal field theories in five dimensions that have duals in massive type IIA supergravity. The localization computations are performed in the non-renormalizable effective field theories obtained through relevant deformations of the UV superconformal field theories. We compare the free energy to a holographic computation of entanglement entropy in the duals and find perfect agreement. In particular, we reproduce the scaling of the free energy that was expected from supergravity.

Paper Structure

This paper contains 8 sections, 36 equations, 1 figure.

Table of Contents

  1. Introduction and overview
  2. Exact 5d SCFT $S^5$ partition function from the IR Lagrangian
  3. Supersymmetric localization results
  4. Simplifications in the large $N$ limit
  5. Matrix model computations
  6. $USp(2N)$ theory with matter
  7. Orbifold theories
  8. Gravity dual and entanglement entropy

Figures (1)

  • Figure 1: The three families of SCFTs discussed in Bergman:2012kr. The dots represent 5d $SU(2N)$ or $USp(2N)$ vector multiplets; the solid orange lines are hyper multiplets in bifundamental representations; and the dashed brown lines are hyper multiplets in the antisymmetric representation. In addition, one may have fundamental hyper multiplets charged under any of the gauge group factors.