Flag manifold sigma-models and nilpotent orbits

Abstract

In the present paper we study flag manifold sigma-models that admit a zero-curvature representation. It is shown that these models may be naturally considered as interacting (holomorphic and anti-holomorphic) $\beta \gamma$-systems. Besides, using the theory of nilpotent orbits of complex Lie groups, we establish a relation to the principal chiral model.

arXiv comment12 pages

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Cited by in corpus (12)

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• Integrable $\mathcal{E}$-Models, 4d Chern-Simons Theory and Affine Gaudin Models. I. Lagrangian Aspects
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• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• Sigma models as Gross-Neveu models
• Integrable degenerate $\mathcal{E}$-models from 4d Chern-Simons theory
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• Deformed $\sigma$-models, Ricci flow and Toda field theories
• Sigma models as Gross-Neveu models. II
• On bosonic Thirring model in Minkowski signature
• On First-Order GLSM for Sigma Models