## The giant graviton expansion in $AdS_5 \times S^5$

Giorgos Eleftheriou, Sameer Murthy, Martí Rosselló

SciPost Phys. 17, 098 (2024) · published 1 October 2024

- doi: 10.21468/SciPostPhys.17.4.098
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### Abstract

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.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Giorgos Eleftheriou, -
^{1}^{2}Sameer Murthy, -
^{3}Martí Rosselló

^{1}King's College London [KCL]^{2}Institute for Advanced Study [IAS]^{3}中央研究院數學所 / Institute of Mathematics, Academia Sinica