Topological Field Theory and Nonlinear $σ$-Models on Symmetric Spaces

Details Topological Field Theory and Nonlinear $σ$-Models on Symmetric Spaces Topological Field Theory and Nonlinear $σ$-Models on Symmetric Spaces

1995-06-20

arxiv.org/abs/hep-th/9506130v1

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX format, 31 pages

Scientific paper

We show that the classical non-abelian pure Chern-Simons action is related to nonrelativistic models in (2+1)-dimensions, via reductions of the gauge connection in Hermitian symmetric spaces. In such models the matter fields are coupled to gauge Chern-Simons fields, which are associated with the isotropy subgroup of the considered symmetric space. Moreover, they can be related to certain (integrable and non-integrable) evolution systems, as the Ishimori and the Heisenberg model. The main classical and quantum properties of these systems are discussed in connection with the topological field theory and the condensed matter physics.

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