Bootstrapping Giant Graviton Correlators

Abstract

We develop bootstrap methods for mixed heavy-light four-point correlators $\langle GGOO\rangle$ in $\mathcal N=4$ super-Yang--Mills theory at large $N$, where $O\equiv {\cal O}_2$ is the chiral primary operator in the stress-tensor multiplet and $G$ are (dual) giant graviton operators with dimension of order $N$, including the maximal determinant case. The loop integrand is expanded in a basis of labelled $f$-graphs -- necessarily including non-planar topologies due to the dimension-$N$ nature of the giant gravitons -- and the coefficients are fixed by various bootstrap conditions including double-triangle and triangle rules in the cusp and OPE limits, integrated correlators from supersymmetric localization, and a ten-dimensional hidden symmetry, the latter also allowing extension to correlators involving generic chiral primaries $\mathcal{O}_k$. Together, these inputs uniquely determine the correlator through three loops, passing further non-trivial consistency checks. For the maximal determinant operator, we reproduce the known results through two loops and obtain the full three-loop correction.