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

## TL;DR

This paper studies finite N corrections to the superconformal index of orbifold quiver gauge theories within the AdS/CFT framework, confirming that D3-branes wrapped on specific cycles reproduce these corrections.

## Contribution

It establishes a detailed correspondence between baryonic charges and D3-brane wrapping numbers, confirming the supergravity predictions with gauge theory calculations for leading finite N corrections.

## Key findings

- Complete agreement between gauge theory and gravity calculations for leading finite N corrections.
- Identification of D3-brane wrapping cycles corresponding to baryonic charges.
- Validation of the superconformal index's finite N corrections via localization and holography.

## Abstract

We investigate the AdS/CFT correspondence for quiver gauge theories realized on D3-branes put on abelian orbifolds by using the superconformal index. We assume that on the gravity side the finite $N$ corrections of the index are reproduced by D3-branes wrapped on three particular three-cycles in the internal space ${\cal Y}$, the abelian orbifold of $\boldsymbol{S}^5$. We first establish the relation between baryonic charges on the gauge theory side and the D3-brane wrapping numbers and holonomies on D3-branes. Then we confirm our proposal by comparing the results of localization for gauge theories and the results on the AdS side including the contributions of D3-branes and excitation on them for many examples. We only focus on the leading finite $N$ corrections starting from $q^N$, and leave the sub-leading corrections starting at $q^{kN}$ ($k\geq2$) as a task for the future. We find complete agreement for the leading corrections in all examples.