1999/05/11 by H. Saleur, Hubert Saleur · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Integrable system #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Particle physics #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Spin (aerodynamics) #Supersymmetry #cond-mat #hep-th #nlin.SI #solv-int
paper · pdf · doi:10.1016/s0550-3213(00)00002-x
published as Nucl.Phys. B578 (2000) 552-576
arxiv created 1999/05/11 · openalex publication_date 2000/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I discuss in this paper the continuum limit of integrable spin chains based on the superalgebras sl(N/K). The general conclusion is that, with the full ``supersymmetry'', none of these models is relativistic. When the supersymmetry is broken by the generator of the sub u(1), Gross Neveu models of various types are obtained. For instance, in the case of sl(N/K) with a typical fermionic representation on every site, the continuum limit is the GN model with N colors and K flavors. In the case of sl(N/1) and atypical representations of spin j, a close cousin of the GN model with N colors, j flavors and flavor anisotropy is obtained. The Dynkin parameter associated with the fermionic root, while providing solutions to the Yang Baxter equation with a continuous parameter, thus does not give rise to any new physics in the field theory limit. These features are generalized to the case where an impurity is embedded in the system.