Abstract
The two-dimensional non-linear σ model on a Riemannian symmetric spaceM=G/H is coupled to fermions with quartic self-interactions. The resulting hybrid model is presented in a gauge-dependent formulation, with a bosonic field taking values inG and a fermionic field transforming under a given representation of the gauge groupH. General criteria for classical integrability are presented: they essentially fix the Lagrangian of the model but leave the fermion representation completely arbitrary. It is shown that by a special choice for the fermion representation (derived from the adjoint representation ofG by an appropriate reduction) one arrives naturally at the supersymmetric non-linear σ model onM=G/H. The issue of quantum integrability is also discussed, though with less stringent results.
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Lüscher, M.: Private communication
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Communicated by G. Mack
Work partially supported by CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico), Brazil, and KFA Jülich, Federal Republic of Germany
On leave of absence from Fakultät für Physik der Universität Freiburg, Federal Republic of Germany
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Abdalla, E., Forger, M. Integrable non-linear σ models with fermions. Commun.Math. Phys. 104, 123–150 (1986). https://doi.org/10.1007/BF01210796
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DOI: https://doi.org/10.1007/BF01210796