Exact results for 5d SCFTs of long quiver type

TL;DR

This work derives exact large-N results for 5d SCFTs with Type IIB holographic duals by translating squashed S^5 partition functions into long-quiver matrix models and solving their saddle points via a 2d electrostatics analogy. The authors obtain closed-form free energies for a wide class of theories, including +_{N,M}, T_N, Y_N, and constrained junctions such as T_{N,K,j} and +_{N,M,j}, with special attention to N_f=2N interior nodes. A universal relation C_T = -640/π^2 F_{S^5} is established, linking conformal central charges to sphere free energies in the large-N limit, and numerous results are shown to agree with AdS_6/CFT_5 predictions and prior numerical studies. The analysis also reveals how polylogarithmic structures arise in theories with interior flavors, and demonstrates the consistency of various S-dual descriptions within Type IIB brane constructions. Overall, the paper provides a comprehensive analytic toolkit for exact large-N observables of long-quiver 5d SCFTs and strengthens the bridge between field theory and holographic duals.

Abstract

Exact results are derived for 5d SCFTs with holographic duals in Type IIB supergravity. These theories have relevant deformations that flow to linear quiver gauge theories, with the number of nodes large in the large-$N$ limits described by supergravity. Starting from a suitable formulation of the matrix models resulting from supersymmetric localization of the squashed $S^5$ partition functions, the saddle point equations are solved for generic quivers with $N_f=2N$ at all interior nodes, which includes the $T_N$ theories, and for a sample of theories with $N_f\neq 2N$ nodes including theories with Chern-Simons terms. The resulting exact expressions for the free energies and conformal central charges are consistent with supergravity predictions and, where available, with previous numerical field theory analyses.

Figures (4)

• Figure 1: Schematic form of the electrostatic problem associated with a generic quiver. At $z=0$ and $z=1$ Dirichlet boundary conditions are imposed, which are vanishing aside from $\delta$-functions at the marked points. The black dots at $x=0$ represent point charges due to fundamental flavors at interior nodes. The solid lines at $z=z_1$ and $z=z_3$ represent perfectly conducting plates at interior nodes with $N_f\neq 2N$, with total charge given by the discontinuity in $\partial_z N(z)$. The node at $z=z_3$ has maximal Chern-Simons level, so that the support of $\varrho$ is bounded only on one side; the Chern-Simons level at the $z=z_1$ node is smaller.
• Figure 2: 5-brane junctions for the $+_{N,M}$, $T_N$, $Y_N$ and $\diagup\!\!\!\!\!{+}_N$ theories from left to right. $(p,q)$ 5-branes are represented by straight lines at angles determined by the $p,q$ charges, the filled black dots represent corresponding $[p,q]$ 7-branes. The 5d SCFTs are realized by intersections at a point; the external 5-branes have been resolved slightly to visually represent the involved branes.
• Figure 3: $Y_N$ junction with the central node of the quiver deformation (\ref{['eq:YN-quiver-2']}) partly resolved. The solid lines show the subweb correspobding to the central node; it can be obtained from a $+_{N,2}$ web by integrating out two flavors. The quiver tails correspond to the dashed lines.
• Figure 4: Constrained 5-brane junctions with multiple 5-branes ending on the same 7-branes. From left to right for the $T_{2K,K,2}$, $T_{N,K,j}$, and $+_{N,M,j}$ theories.