Quantum flag manifold $\sigma$-models and Hermitian Ricci flow

Abstract

We show that flag manifold $\sigma$-models (including ${\mathbb{CP}}^{n-1}$, Grassmannian models as special cases) and their deformed versions may be cast in the form of gauged bosonic Thirring/Gross-Neveu-type systems. Quantum mechanically the gauging is violated by chiral anomalies, which may be cancelled by adding fermions. We conjecture that such models are integrable and check on some examples that the trigonometrically deformed geometries satisfy the generalized Ricci flow equations.

41 pages, 6 figures

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Cited by in corpus (9)

• Flag manifold sigma models: spin chains and integrable theories
• On the Zakharov-Mikhailov action: $4$d Chern-Simons origin and covariant Poisson algebra of the Lax connection
• Sigma models as Gross-Neveu models
• Sigma models with local couplings: a new integrability -- RG flow connection
• Integrable sigma models on Riemann surfaces
• Monopole harmonics on ${\mathbb{CP}}^{n-1}$
• Grassmannian Sigma Models
• Nonperturbative features in the Lie-algebraic Kähler sigma model with fermions
• $\beta$-function of the level-zero Gross-Neveu model