  We introduce a nonperturbative approach to correlation functions of two
determinant operators and one non-protected 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 worldsheet between an integrable
boundary state and a state dual to the single-trace operator. We determine the
boundary state using symmetry and integrability of the dual superstring sigma
model, and write down expressions for the correlators at finite coupling, which
we conjecture to be valid for operators of arbitrary size. The proposal is put
to test at weak coupling.
