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Motivated by understanding the scattering of gravitons and theirsuperpartners from extended $(p, q)$-strings in type IIB string theory viaAdS/CFT, we study an integrated two-point function of stress tensor multipletoperators in the presence of a half-BPS line defect in ${\cal N} = 4$ $SU(N)$super-Yang-Mills theory. We determine this integrated correlator at the fivelowest non-trivial orders in $1/\sqrt{N}$ at fixed Yang-Mills coupling and$\theta$ angle. Our calculations are performed explicitly when the line defectis a Wilson line, in which case we find a finite number of perturbativecontributions at each order in $1/\sqrt{N}$, as well as instantoncontributions. Using $SL(2, \mathbb{Z})$ transformations, our results can alsobe applied to Wilson-'t Hooft line defects dual to extended $(p, q)$-strings inthe bulk. We analyze features of these integrated correlators in the weakcoupling expansion by comparing with open-closed amplitudes of type IIB stringtheory on $\text{AdS}_5\times \text{S}^5$, as well as in its flat space limit.We predict new higher-derivative interaction vertices on the D1-brane and, moregenerally, on $(p,q)$-strings.

Scattering From $(p,q)$-Strings in $\text{AdS}_5 \times \text{S}^5$