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Integrable properties of sigma-models with non-symmetric target spaces
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It is well-known that sigma-models with symmetric target spaces are classically integrable. At the example of the model with target space the flag manifold U(3)/U(1)^3 -- a non-symmetric space -- we show that the introduction of torsion allows to cast the equations of motion in the form of a zero-curvature condition for a one-parametric family of connections, which can be a sign of integrability of the theory. We also elaborate on geometric aspects of the proposed model.
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Cited by 2 Pith papers
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Gauge Theory And Integrability, III
A four-dimensional Chern-Simons gauge theory with surface defects systematically engineers two-dimensional integrable field theories with Lax operators.
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Ultralocal Lax connection for para-complex $\mathbb{Z}_T$-cosets
Classical sigma-models on para-complex Z_T-cosets admit an ultralocal, gauge-invariant Lax connection whose light-cone components Poisson-commute, extending earlier results for hermitian symmetric spaces.
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