Exchange relations and crossing

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 Φ 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>A</mml:mi> <mml:mi>d</mml:mi> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>T</mml:mi> <mml:mn>4</mml:mn> </mml:msup> </mml:mrow> </mml:math> 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.