Strong Wilson polygons from the lodge of free and bound mesons

Previously predicted by the S-matrix bootstrap of the excitations over theGKP quantum vacuum, the appearance of a new particle at strong coupling, formedby one fermion and one anti-fermion, is here confirmed: this two-dimensional mesonshows up, along with its infinite tower of bound states, while analysing the fermioniccontributions to the Operator Product Expansion (collinear regime) of the Wilson nullpolygon loop. Moreover, its existence, free and bound, turns out to be a powerful ideain re-summing all the contributions (at large coupling) for a general n-gon (n greater than 6) to aThermodynamic Bethe Ansatz, which is proven to be equivalent to the known one andsuggests new structures for a special Y -system.