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

Motivated by understanding the scattering of gravitons and their superpartners from extended $(p,q)$-strings in type IIB string theory via AdS/CFT, we study an integrated two-point function of stress tensor multiplet operators in the presence of a half-BPS line defect in $\mathcal{N}=4$ $SU(N)$ super-Yang-Mills theory. We determine this integrated correlator at the five lowest non-trivial orders in $1\mathrm{/}\sqrt{N}$ at fixed Yang-Mills coupling and $\theta$ angle. Our calculations are performed explicitly when the line defect is a Wilson line, in which case we find a finite number of perturbative contributions at each order in $1\mathrm{/}\sqrt{N}$, as well as instanton contributions. Using $SL(2,\mathbb{Z})$ transformations, our results can also be applied to Wilson-'t Hooft line defects dual to extended $(p,q)$-strings in the bulk. We analyze features of these integrated correlators in the weak coupling expansion by comparing with open-closed amplitudes of type IIB string theory 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, more generally, on $(p,q)$-strings.