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

TL;DR

This paper provides a holographic interpretation of the superconformal index in N=4 super Yang-Mills theory by relating it to giant graviton configurations in AdS_5 x S^5, revealing a new connection between gauge theory and string theory states.

Contribution

It derives a bulk interpretation of the superconformal index series through giant graviton configurations and their quantum mechanics, connecting gauge theory indices to string theory objects.

Findings

The superconformal index series corresponds to giant graviton configurations in AdS_5 x S^5.

The quadratic fluctuations of a maximal giant are described by a supersymmetric Landau problem.

Multiple giants are represented by matrix versions of the supersymmetric quantum mechanics.

Abstract

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.