Flavor symmetries of six-dimensional ${\cal N}=(1,0)$ theories from AdS/CFT correspondence

TL;DR

This paper computes superconformal indices for 6D ${ m (1,0)}$ theories on M5-branes at singularities using AdS/CFT, incorporating finite N corrections from wrapped M2-branes, confirming flavor symmetry expectations.

Contribution

It introduces a method to calculate superconformal indices of 6D ${ m (1,0)}$ theories with finite N corrections via AdS/CFT, linking geometry and flavor symmetries.

Findings

Superconformal indices match expected flavor symmetries.

Finite N corrections from wrapped M2-branes are successfully included.

Method confirms consistency of holographic duals with field theory.

Abstract

We calculate the superconformal indices of a class of six-dimensional ${\cal N}=(1,0)$ superconformal field theories realized on M5-branes at $\mathbb{C}^2/\mathbb{Z}_k$ singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite $N$ corrections are included as the contribution of M2-branes wrapped on two-cycles in $S^4/\mathbb{Z}_k$. We confirm that the indices are consistent with the expected flavor symmetries.