On the integrability of N = 2 supersymmetric massive theories

Abstract

In this paper we propose a criterion to establish the integrability of N = 2 supersymmetric massive theories. The basic data required are the vacua and the spectrum of Bogomolnyi solitons, which can be neatly encoded in a graph (nodes=vacua and links=Bogomolnyi solitons). Integrability is then equivalent to the existence of solutions of a generalized Yang-Baxter equation which is built up from the graph (graph-Yang-Baxter equation). We solve this equation for two general types of graphs: circular and daisy, proving, in particular, the integrability of the following Landau-Ginzburg superpotentials: A n ( t 1), A n ( t 2), D n ( τ), E 6( t 7) and E 8( t 16). For circular graphs the solution are intertwiners of the affine Hopf algebra U q( A 1 (1)) , while for daisy graphs the solution corresponds to a SUSY generalization of the Boltzmann weights of the chiral Potts model in the trigonometric regime. A chiral-Potts-like solution is conjectured for the more tricky case D n ( t 2). The scattering theory of circular models, for instance A n ( t 1) or D n ( τ), is Toda-like. The physical spectrum of daisy models, as A n ( t 2), E 6( t 7) or E 8( t 16), is given by confined states of radial solitons. The scattering theory of the confined states is again Toda-like. Bootstrap factors for the confined solitons are given by fusing the SUSY chiral Potts S-matrices of the elementary constituents; i.e the radial solitons of the daisy graph.