Finite $N$ corrections to the superconformal index of toric quiver gauge theories

TL;DR

This paper derives a formula for finite N corrections to the superconformal index of toric quiver gauge theories using AdS/CFT correspondence, focusing on single D3-brane wrapped configurations and confirming predictions with gauge theory calculations.

Contribution

It introduces a new formula for finite N corrections to the superconformal index based on D3-brane wrapped configurations in toric Calabi-Yau cones.

Findings

The formula accurately predicts finite N corrections for several examples.

Comparison with localization results confirms the formula's validity.

The approach focuses on single brane wrapping, excluding multiple wrappings.

Abstract

The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi-Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite $N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small size of gauge groups, and confirm that the formula correctly reproduces the finite $N$ corrections up to expected order.