Structure constants of a single trace operator and determinant operators from hexagon

We investigate the structure constant associated with a single trace operator and two determinant operators in N = 4 super Yang–Mills theory. In the holographic framework, this quantity corresponds to the interaction vertex between a closed string and two open strings attached to spherical D -branes. Based on diagrammatic intuition, we propose a conjecture that the structure constant at finite coupling can be elegantly expressed in terms of hexagon form factors. Specifically, this involves the preparation of two hexagon twist operators and the appropriate gluing of edges by integrating contributions from mirror particles and contracting boundary states. The gluing process yields the worldsheet for a closed string and two open strings attached to the D -branes. At weak coupling, the asymptotic expression simplifies to a sum over all possible partitions, not only for the edge related to the closed string but also for the edges representing half of the open string, taking into account reflection effects for the opposite open string edges. We validate this conjecture by directly computing various tree-level structure constants, and our results align well with the proposed conjecture. In particular, we find that there are multiple contractions in the tree-level problem as in four-point function problems. This is consistent with the fact that the worldsheet we are studying has one-dimensional moduli space.