Integrable Chiral Theories in 2+1 Dimensions
D. Gianzo, J.O. Madsen, J. Sanchez Guillen
TL;DR
This paper introduces new integrable Lorentz invariant submodels of the principal chiral model in 2+1 dimensions, featuring infinite conserved currents, with explicit constructions for su(2) and su(3), and discusses potential applications to supersymmetric models.
Contribution
It presents a novel method for constructing integrable submodels in higher dimensions based on zero curvature, extending to any Lie algebra and dimension.
Findings
Explicit conserved currents for su(2) case
Construction applicable to any Lie algebra
Potential applications to supersymmetric models
Abstract
Following a recent proposal for integrable theories in higher dimensions based on zero curvature, new Lorentz invariant submodels of the principal chiral model in 2+1 dimensions are found. They have infinite local conserved currents, which are explicitly given for the su(2) case. The construction works for any Lie algebra and in any dimension, and it is given explicitly also for su(3). We comment on the application to supersymmetric chiral models.
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