Holographic index calculation for Argyres-Douglas and Minahan-Nemeschansky theories

TL;DR

This paper computes superconformal indices for certain $ ext{AdS}_5/ ext{CFT}_4$ theories, incorporating finite-$N$ corrections from wrapped D3-branes, and finds results consistent with known data for small N.

Contribution

It provides explicit superconformal index calculations for Argyres-Douglas and Minahan-Nemeschansky theories, including finite-$N$ effects via wrapped D3-branes, which is a novel approach.

Findings

Explicit index results for N=1,2,3

Good agreement with known results for small N

Finite-N corrections from wrapped D3-branes are significant

Abstract

We calculate the superconformal indices of the $\mathcal N=2$ superconformal field theories realized on $N$ coincident D3-branes in 7-brane backgrounds with constant axiodilaton via the AdS/CFT correspondence. We include the finite-$N$ corrections as the contribution of D3-branes wrapped around 3-cycles in the internal space. We take only single-wrapping contributions into account for simplicity. We also determine the orders of the next-to-leading corrections which we do not calculate. The orders are relatively high, and we obtain many trustable terms. We give the results for $N=1,2,3$ explicitly, and find nice agreement with known results.