Spinning hexagons

bstract We reduce the computation of three point function of three spinning operators with arbitrary polarizations in 𝒩 = 4 SYM to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the hexagon partition function . We explore its analytic structure and use it to generate perturbative data for spinning three point functions. For certain polarizations and any coupling, we express the full asymptotic three point function in determinant form. With the integrability approach established we open the ground to study the large spin limit where dualities with null Wilson loops and integrable pentagons must appear.