Exact S-matrices for supersymmetric sigma models and the Potts model

Details Exact S-matrices for supersymmetric sigma models and the Potts model Exact S-matrices for supersymmetric sigma models and the Potts model

2002-07-19

arxiv.org/abs/hep-th/0207176v1

J. Phys. A 35 (2002) 10675

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, 8 figures

Scientific paper

10.1088/0305-4470/35/50/301

We study the algebraic formulation of exact factorizable S-matrices for integrable two-dimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie ``supersymmetry'' algebras sl(m+n|n) (m=1,2; n>0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These S-matrices represent the perturbation of the conformal theory at theta=pi by a small change in the topological angle theta. The m=1, n=1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for theta=0 and theta=pi, in certain other supersymmetric sigma models.

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