Classical Integrability for Three-point Functions: Cognate Structure at Weak and Strong Couplings

Understand

In this paper, we develop a new method of computing three-point functions in the SU(2) sector of the $\mathcal{N}=4$ super Yang-Mills theory in the semi-classical regime at weak coupling, which closely parallels the strong coupling analysis.

• The structure threading two disparate regimes is the so-called monodromy relation, an identity connecting the three-point functions with and without the insertion of the monodromy matrix.
• We shall show that this relation can be put to use directly for the semi-classical regime, where the dynamics is governed by the classical Landau-Lifshitz sigma model.
• Specifically, it reduces the problem to a set of functional equations, which can be solved once the analyticity in the spectral parameter space is specified.