On the planar limit of 3d Tρσ[SU(N)]

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.

Automated summary

In this study, we discuss 3d T-rho(sigma)[SU(N)] quiver gauge theories with a large number of nodes and ranks scaling quadratically with the length of the quiver. The sphere free energies and topologically twisted indices were obtained using supersymmetric localization, showing quartic scaling with the length of the quiver and quadratic scaling with N. The IR SCFTs have supergravity duals in Type IIB, with free energies matching holographic results and previously discussed theories arising as limiting cases. Each balanced 3d quiver theory is linked to a 5d parent, with close relations between BPS observables dominated by the same saddle point in the matrix model.