Negative Rank Relations for Giant Graviton Correlators

Abstract: We study correlation functions of giant and dual giant gravitons in $\mathcal N=4$ super Yang--Mills theory. Although the two objects correspond to rather different D3 brane configurations in $AdS_5\times S<sup>5$, their gauge theory operators are Schur polynomials associated with transposed Young diagrams. We show that this transposition is accompanied by a formal rank reflection $N\to -N$ at the level of correlation functions. For both $U(N)$ and $SU(N)$, the relation is exact for free correlators at finite $N$, and, using Lagrangian insertion, extends to separated point weak coupling integrands at every loop order. More generally, it applies to any number of Schur polynomial external operators, provided all Young diagrams are transposed. We illustrate the relation in several examples and also discuss evidence for its extension beyond perturbative integrands.