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

Abstract

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 anti-de Sitter/conformal field theory 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 that we do not calculate. The orders are relatively high, and we obtain many trustworthy terms. We give the results for N = 1, 2, 3 explicitly, and find nice agreement with known results.