The superconformal index of $\frac12$-BPS states of $N=4$ 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 $AdS_5 \times S^5$. 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.
Author indications on fulfilling journal expectations
Provide a novel and synergetic link between different research areas.
Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
Detail a groundbreaking theoretical/experimental/computational discovery
Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
Changes made as requested.
List of changes
Added comment on the M2 and M5-brane theories at the end of the paper. Typos corrected as listed on the SciPost page.
