Finite-N corrections to the superconformal index of S-fold theories

We study the superconformal index of S-fold theories by using the anti-de Sitter / conformal field theory correspondence. It is known that the index in the large-N limit is reproduced as the contribution of bulk Kaluza-Klein modes. For finite-N, D3-branes wrapped around the non-trivial cycle in S-5/Z(k), which corresponds to Pfaffian-like operators, give the corrections of order q(N) to the index. We calculate the finite-N corrections by analyzing the fluctuations of wrapped D3-branes. Comparisons to known results show that our formula correctly reproduces the corrections up to errors of order q(2N).