The continuum limit of sl(N/K) integrable super spin chains

Abstract

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.

References in corpus (8)

• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• The algebraic Bethe ansatz for rational braid-monoid lattice models
• Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
• An Intersecting Loop Model as a Solvable Super Spin Chain
• Doping of a spin-1 chain: integrable model
• On the solution of a supersymmetric model of correlated electrons
• Tunneling in quantum wires II: A new line of IR fixed points
• Multiparameter Integrable QFT's with N bosons

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• Bethe Ansatz Equations for General Orbifolds of N=4 SYM
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