Contributor info: Prof. Sameer Murthy

Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló

SciPost Phys. 17, 098 (2024) · published 1 October 2024 | Toggle abstract · pdf

The superconformal index of $\frac12$-BPS states of $\mathcal{N}=4$ $U(N)$ super Yang-Mills theory has a known infinite $q$-series expression with successive terms suppressed by $q^N$. We derive a holographic bulk interpretation of this series by evaluating the corresponding functional integral in the dual AdS$_5 × S^5$. The integral localizes to a product of small fluctuations of the vacuum and of the collective modes of an arbitrary number of giant-gravitons wrapping an $S^3$ of maximal size inside the $S^5$. The quantum mechanics of the small fluctuations of one maximal giant is described by a supersymmetric version of the Landau problem. The quadratic fluctuation determinant reduces to a sum over the supersymmetric ground states, and precisely reproduces the first non-trivial term in the infinite series. Further, we show that the terms corresponding to multiple giants are obtained precisely by the matrix versions of the above super-quantum-mechanics.