Schur index of the $\mathcal{N}=4$ $U(N)$ SYM via the AdS/CFT correspondence

Abstract

We calculate the Schur index of the $\mathcal{N}=4$ $U(N)$ SYM with finite $N$ via the AdS/CFT correspondence as the contribution of D3-branes wrapped on contractible cycles in ${\mathbf{S}}^5$ on some assumptions motivated by preliminary analyses. As far as we have checked numerically it agrees with the index calculated on the gauge theory side. In a certain limit it reproduces the analytic result given by Bourdier, Drukker, and Felix.

arXiv comment10 pages, minor corrections, appendix added, version accepted for PRD

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• Exact Stringy Microstates from Gauge Theories
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• Large $N$ and large representations of Schur line defect correlators
• Flavor symmetries of six-dimensional $\mathcal{N}=(1,0)$ theories from AdS/CFT correspondence
• The giant graviton expansion in $Ad{S}_5\times S^5$
• Giant graviton expansions and ETW brane
• Orbifold ETW brane and half-indices
• M2-M5 giant graviton expansions
• ADHM Wilson line defect indices
• The Giant Graviton Expansion
• Finite-$N$ superconformal index via the AdS/CFT correspondence
• Localization and wall-crossing of giant graviton expansions in AdS${}_5$
• $SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs
• Holographic spectral functions for Sasaki-Einstein 5-manifolds