The strange case of 4D Wilson loops or a third way to TBA

I will show how the relativistic Thermodynamic Bethe Ansatz (TBA) by Al. Zamolodchikov, naturally attached to Dynkin diagrams, can be derived from an operator product expansion of null polygonal Wilson loops. This is a sort of third way by which TBA arises naturally, by counting as other means 1) the usual thermodynamics on the scattering theory and 2) its derivation from the functional equations of the so-called Ordinary Differential Equation/Integrable Models correspondence. I will illustrate both these ways.