Long-range to the rescue of Yang-Baxter

We study the spin chain model which captures the one-loop spectral problem of a prototypical example of an $\mathcal{N}=2$ SCFT in four dimensions.Up to date this spin chain model remains unfathomable; the Yang-Baxter equation is not satisfied and the usual Bethe Ansatz does not lead to a solution from three magnons on. In this paper we find a long range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of our solutions, labeled by two integers, obey an infinite tower of Yang Baxter equations.Our method of solving the three-magnon problem generalises the Bethe Ansatz approach to cases where the permutation symmetry is broken. The long range contributions can be understood as computing corrections away from the plane wave basis.