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Flag manifold sigma models and nilpotent orbits. (English. Russian original) Zbl 1454.70012

Proc. Steklov Inst. Math. 309, 78-86 (2020); translation from Tr. Mat. Inst. Steklova 309, 89-98 (2020).
This work studies flag manifold sigma models introduced by the author earlier [“Complex structures and zero-curvature equations for \(\sigma\)-models”, Phys. Lett. B 760, 341–344 (2016)]. It is shown that these models can be alternatively formulated as two coupled \(\beta\gamma\)-systems interacting via an auxiliary field. This proves the equivalence of these models and the flag manifold models.
This work also investigates the relation between the flag manifold sigma models and the principal chiral model. It is demonstrated that the solutions of the principal chiral model that define a map into the nilpotent orbit of the corresponding complexified Lie group, correspond to solutions of the flag manifold sigma model.

MSC:

70S20 More general nonquantum field theories in mechanics of particles and systems
81T10 Model quantum field theories
70G65 Symmetries, Lie group and Lie algebra methods for problems in mechanics
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