Exchange relations and crossing

TL;DR

This paper explores how non-trivial exchange relations in 2D integrable QFTs modify crossing equations, enabling the construction of new S-matrices and simplifying the massless dressing factor in superstring models.

Contribution

It proposes a consistent modification to crossing equations for models with exchange relations, verified through examples like the $SU(N)$ Gross-Neveu model and massless superstring excitations.

Findings

Modified crossing equations for models with exchange relations.

Agreement with existing proposals for specific models.

Simplified massless dressing factor in superstring theory.

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.