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We study the superconformal index of S-fold theories by using AdS/CFTcorrespondence. It has been known that the index in the large $N$ limit isreproduced as the contribution of bulk Kaluza-Klein modes. For finite $N$D3-branes wrapped around the non-trivial cycle in$\boldsymbol{S}^5/\mathbb{Z}_k$, 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 toknown results show that our formula correctly reproduces the corrections up toerrors of order $q^{2N}$.

Finite $N$ Corrections to the Superconformal Index of S-fold Theories