Strong Wilson polygons from the lodge of free and bound mesons

Previously predicted by the $S$-matrix bootstrap of the excitations over the GKP quantum vacuum, the appearance of a new particle at strong coupling -- formed by one fermion and one anti-fermion -- is here confirmed: this two-dimensional meson shows up, along with its infinite tower of bound states, while analysing the fermionic contributions to the Operator Product Expansion (collinear regime) of the Wilson null polygon loop. Moreover, its existence, free \footnote{This term is used here as opposite to bound, thus as {\it unbound}.} and bound, turns out to be a powerful idea in re-summing all the contributions (at large coupling) for a general $n$-gon ($n\geq 6$) to a Thermodynamic Bethe Ansatz, which is proven to be equivalent to the known one and suggests new structures for a special $Y$-system.