Finite-N superconformal index via the AdS/CFT correspondence

Abstract

Abstract We propose a prescription to calculate the superconformal index of the ${\cal N}=4$  U(N) supersymmetric Yang–Mills theory with finite N on the anti-de Sitter side. The finite-N corrections are included as contributions of D3-branes wrapped around three-cycles in ${\boldsymbol S}^5$, which are calculated as the index of the gauge theories realized on the wrapped branes. The single-wrapping contribution has been studied in a previous work, and we further confirm that the inclusion of multiple-wrapping contributions correctly reproduces the higher-order terms as far as we have checked numerically.