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

Abstract

We study the superconformal index of S-fold theories by using AdS/CFT correspondence. It has been 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 ${\mathbf{S}}^5/{\mathbb{Z}}_k$, 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 to known results show that our formula correctly reproduces the corrections up to errors of order $q^{2N}$.

arXiv comment66 pages, 2 figures; minor modifications, version accepted for publication for PTEP

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• Exact Stringy Microstates from Gauge Theories
• An N=1 Lagrangian for an N=3 SCFT
• Finite $N$ corrections to the superconformal index of toric quiver gauge theories
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• Finite $N$ indices and the giant graviton expansion
• Flavor symmetries of six-dimensional $\mathcal{N}=(1,0)$ theories from AdS/CFT correspondence
• Giant graviton expansions and ETW brane
• Orbifold ETW brane and half-indices
• Exceptional moduli spaces for exceptional $\mathcal{N}=3$ theories
• Macdonald Indices for Four-dimensional $\mathcal{N}=3$ Theories
• M2-M5 giant graviton expansions
• Localization and wall-crossing of giant graviton expansions in AdS${}_5$
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Holographic spectral functions for Sasaki-Einstein 5-manifolds