Exact Three-Point Functions of Determinant Operators in Planar $N=4$ Supersymmetric Yang-Mills Theory

We introduce a nonperturbative approach to correlation functions of two determinant operators and one nonprotected single-trace operator in planar N=4 supersymmetric Yang-Mills theory. Based on the gauge-string duality, we propose that they correspond to overlaps on the string world sheet between an integrable boundary state and a state dual to the single-trace operator. We determine the boundary state using the symmetry and integrability of the dual superstring σ model and write expressions for the correlators at finite coupling, which we conjecture to be valid for operators of arbitrary size. The proposal is put to the test at weak coupling.