On the planar limit of 3d $T_\rho^\sigma[SU(N)]$

TL;DR

This paper analyzes a large N limit of 3d $T_ ho^\sigma[SU(N)]$ quiver gauge theories, revealing scaling behaviors of free energies and indices, and establishing holographic duals and relations to 5d theories.

Contribution

It introduces a new large N limit for 3d quiver theories with quadratic rank scaling, providing exact localization results and holographic dual descriptions.

Findings

Sphere free energies scale quartically with quiver length and quadratically with N.

Matching results between field theory and supergravity holography.

Connections established between 3d quivers and 5d parent theories.

Abstract

We discuss a limit of 3d $T_\rho^\sigma[SU(N)]$ quiver gauge theories in which the number of nodes is large and the ranks scale quadratically with the length of the quiver. The sphere free energies and topologically twisted indices are obtained using supersymmetric localization. Both scale quartically with the length of the quiver and quadratically with $N$, with trilogarithm functions depending on the quiver data as coefficients. The IR SCFTs have well-behaved supergravity duals in Type IIB, and the free energies match precisely with holographic results. Previously discussed theories with $N^2\ln N$ scaling arise as limiting cases. Each balanced 3d quiver theory is linked to a 5d parent, whose matrix model is related and dominated by the same saddle point, leading to close relations between BPS observables.