Supersymmetric integrable theories without particle production

Abstract

We consider a theory of scalar superfields in two dimensions with arbitrary superpotential. By imposing no particle production in tree-level scattering, we constrain the form of the admissible interactions, recovering a supersymmetric extension of the sinh-Gordon model.

S-matrix bootstrap: Supersymmetry, Z2 , and Z4 symmetry

“…These S-matrices are most likely not physical S-matrices but perhaps they are close enough to physical S-matrices with very little particle production. Finally, note that all this seems to be consistent with the classical intuition from [9] where it was found that the only supersymmetric model with a single real scalar boson and a Majorana fermion, with a Lagrangian description and without tree level particle production is the SSG model. Would be interesting to see if the blue cusps admits a Lagrangian description in terms of a fermion plus a pseudoscalar.…”

“…Would be very interesting to explore other setups with different symmetries and space-time dimensions to better shed light over these puzzles and to best understand how universal they really are. One very concrete avenue for analytic progress is to zoom in on the vertices close to free theories and see if there is still some interesting Lagrangian games to be played a la [9,13]. Would be nice to see if such simple perturbative games, combined with some important bootstrap intuition, could lead to the discovery of new interesting theories.…”

No particle production in two dimensions: recursion relations and multi-Regge limit

“…Since the external particles can be arbitrary, this requirement clearly fixes all n-point vertices for n ≥ 5 in terms of the cubic and quartic couplings. We would like to find the recursion relation on the couplings analogous to (8), using the obvious analogue of the multi-Regge limit (6). We consider the scattering of n particles of species α 1 , .…”

Holographic four-point functions in Toda field theories in AdS2

“…In flat spacetime, two basic consequences of higher conservation laws are the absence of particle production and factorization of the higher-point S-matrix [1,2,3,4]. Since a Lax pair is in general hard to find, no treelevel particle production is regarded as an important sign of classical integrability, and it is a useful strategy for building classically integrable theories [5,6,2,7,8].…”