Leading large N giant graviton correction to Schur correlators in large representations

Abstract

We consider 4d $N=4$ $U\left(N\right)$ SYM and the leading giant graviton correction at large N to the Schur defect 2-point functions of $\frac{1}{2}$-BPS Wilson lines in rank-k symmetric and antisymmetric representations. We study in particular the large k limit for the symmetric case and the regime $1\ll k\ll N$ in the antisymmetric one. In both cases we present exact results for the correction. Wilson lines in symmetric/antisymmetric representations admit a description in terms of D3_k and D5_k brane probes representing a collection of k fundamental strings. In this picture, giant graviton corrections come from fluctuations of brane probes in the presence of a wrapped D3 brane giant graviton. In the antisymmetric case, our leading correction matches the half-index of the 4d $N=4$ Maxwell theory living on the disk which is a part of the giant graviton divided out by the D5_k probe, as recently proposed in arXiv:2404.08302. For the symmetric case at large k, we derive an explicit exact residue formula for the leading large N correction.