Leading Giant graviton expansion of Schur correlators in large representations

TL;DR

This paper computes the leading giant graviton correction to Schur defect 2-point functions in 4d $ ext{N}=4$ $U(N)$ SYM, revealing exact results and connections to brane probe fluctuations and 3d gauge theories.

Contribution

It provides the first exact residue formula for giant graviton corrections to Schur correlators in large symmetric representations.

Findings

Exact correction results agree with matrix model evaluations.

Leading correction matches the half-index of 3d $ ext{N}=4$ Maxwell theory.

Derived explicit residue formula for symmetric case at large $k$.

Abstract

We consider 4d $\mathcal N=4$ $U(N)$ SYM and the leading giant graviton correction 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. We present exact results for the correction in agreement with matrix model evaluation at finite $N,k$. The 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 presence of a wrapped D3 brane giant graviton. In particular, for the antisymmetric case, our leading correction matches the half-index of the 3d $\mathcal N=4$ Maxwell theory living on the 3d 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 correction.