Schur line defect correlators and giant graviton expansion

Abstract

We consider Schur line defect correlators in four dimensional $\mathcal N=4$ $U(N)$ SYM and their giant graviton expansion encoding finite $N$ corrections to the large $N$ limit. We compute in closed form the single giant graviton contribution to correlators with general insertions of $\frac{1}{2}$-BPS charged Wilson lines. For the 2-point function with fundamental and anti-fundamental Wilson lines, we match the result from fluctuations of two half-infinite strings ending on the giant graviton, recently proposed in arXiv:2403.11543. In particular, we prove exact factorization of the defect contribution with respect to wrapped D3 brane fluctuations representing the single giant graviton correction to the undecorated Schur index. This follows from a finite-difference representation of the Schur line defect index in terms of the index without defects, and similar factorization holds quite generally for more complicated defect configurations. In particular, the single giant graviton contribution to the 4-point function with two fundamental and two anti-fundamental lines is computed and discussed in this perspective.