Flag manifold sigma-models: the 1/N-expansion and the anomaly two-form

Abstract

We construct a gauged linear sigma-model representation and develop a 1/N-expansion for flag manifold sigma-models previously proposed by the author. Classically there exists a zero-curvature representation for the equations of motion of these models, which leads in particular to the existence of a conserved non-local charge. We show that at the quantum level this charge is no longer conserved and calculate explicitly the anomaly in its conservation law.

arXiv comment62 pages, 14 figures

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Cited by in corpus (11)

• Dressing cosets and multi-parametric integrable deformations
• Flag manifold sigma models: spin chains and integrable theories
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• Flag manifold sigma-models and nilpotent orbits
• Ultralocal Lax connection for para-complex ${\mathbb{Z}}_T$-cosets
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• An Index for Quantum Integrability
• Lax pairs for new ${\mathbb{Z}}_N$-symmetric coset $\sigma$-models and their Yang-Baxter deformations
• Ricci-flat metrics on vector bundles over flag manifolds
• General Composite Non-Abelian Strings and Flag Manifold Sigma Models
• Quantum cohomology of symplectic flag manifolds