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

Abstract

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.

32 pages, 8 figures

References in corpus (2)

• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Quantum and classical localisation, the spin quantum Hall effect and generalisations

Cited by in corpus (24)

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• Critical exponents of domain walls in the two-dimensional Potts model
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• From the XXZ chain to the integrable Rydberg-blockade ladder via non-invertible duality defects
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Dynamical correlations and quantum phase transition in the quantum Potts model
• Critical points in coupled Potts models and critical phases in coupled loop models
• Logarithmic Superconformal Minimal Models
• Fusion hierarchies, T-systems and Y-systems of logarithmic minimal models
• Bulk and boundary critical behaviour of thin and thick domain walls in the two-dimensional Potts model
• Asymptotic scattering and duality in the one-dimensional three-state quantum Potts model on a lattice
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Tutte chromatic identities from the Temperley-Lieb algebra
• Higher-spin conserved currents in supersymmetric sigma models on symmetric spaces
• Multi-state asymmetric simple exclusion processes
• SO(3) Homology of Graphs and Links
• Critical behaviour of loop models on causal triangulations
• Finite size lattice results for the two-boundary Temperley--Lieb loop model
• Finite volume analysis of scattering theory in the scaling Potts model
• Integrability of planar-algebraic models
• Integrable models from singly generated planar algebras
• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models