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

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 $ \mathcal{Y} $ , the abelian orbifold of 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 ≥ 2) as a task for the future. We find complete agreement for the leading corrections in all examples.