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arXiv · 2408.03365

Long-range to the Rescue of Yang-Baxter

Deniz N Bozkurt·Juan Miguel Nieto García·Elli Pomoni
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Abstract

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 coordinate Bethe Ansatz does not lead to a solution from three magnons on, as the Yang-Baxter equation is not satisfied by the two-magnon scattering coefficients. In this paper, we find a long-range solution to the eigenvalue problem for three magnons. Remarkably, the scattering coefficients of our solution together with the position-dependent corrections, obey an infinite tower of Yang-Baxter equations. Our method of solving the three-magnon problem is interesting in its own right and generalizes the coordinate Bethe Ansatz approach to cases where the permutation symmetry is broken.

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Deniz N Bozkurt, Juan Miguel Nieto García, Elli Pomoni. 2024-08-06. Long-range to the Rescue of Yang-Baxter. https://arxiv.org/abs/2408.03365

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