TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.4.098
TI  - The giant graviton expansion in $AdS_5 \times S^5$
PY  - 2024/10/01
UR  - https://scipost.org/SciPostPhys.17.4.098
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 4
SP  - 098
A1  - Eleftheriou, Giorgos
AU  - Murthy, Sameer
AU  - Rosselló, Martí
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.17.4.098,
	title={{The giant graviton expansion in $AdS_5 \times S^5$}},
	author={Giorgos Eleftheriou and Sameer Murthy and Martí Rosselló},
	journal={SciPost Phys.},
	volume={17},
	pages={098},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.4.098},
	url={https://scipost.org/10.21468/SciPostPhys.17.4.098},
}