Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function

Understand

We develop a novel nonperturbative approach to a class of three-point functions in planar $\mathcal{N}=4$ SYM based on Thermodynamic Bethe Ansatz (TBA).

• More specifically, we study three-point functions of a non-BPS single-trace operator and two determinant operators dual to maximal Giant Graviton D-branes in AdS$_5\times$S$^{5}$.
• They correspond to disk one-point functions on the worldsheet and admit a simpler and more powerful integrability description than the standard single-trace three-point functions.
• We first introduce two new methods to efficiently compute such correlators at weak coupling; one based on large $N$ collective fields, which provides an example of open-closed-open duality discussed by Gopakumar, and the other based on combinatorics.