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arXiv · 2506.04096

Exchange relations and crossing

Sergey Frolov·Davide Polvara·Alessandro Sfondrini
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Abstract

We discuss the scattering matrix of two-dimensional integrable QFTs whose fields obey non-trivial exchange relations. We show that crossing equations for such models have to be modified, and propose their consistent modification. This modification opens the way to constructing new integrable S~matrices. As a check, we consider the crossing equations for the $SU(N)$ chiral Gross-Neveu model, and for the $\Phi_{21}$ deformation of the tricritical Ising model, finding an agreement with the existing proposals. Finally, we reconsider the crossing equations for massless excitations of the mixed-flux $AdS_3\times S^3\times T^4$ light-cone gauge superstring sigma model, and conjecture that the massless excitations satisfy non-trivial exchange relations. This changes the crossing equations and leads to a simpler massless dressing factor.

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Sergey Frolov, Davide Polvara, Alessandro Sfondrini. 2025-06-04. Exchange relations and crossing. https://arxiv.org/abs/2506.04096

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