Grassmannian Sigma Models

Abstract

We show that sigma models with orthogonal and symplectic Grassmannian target spaces admit chiral Gross-Neveu model formulations, thus extending earlier results on unitary Grassmannians. As a first application, we calculate the one-loop $\beta$-functions in this formalism, showing that they are proportional to the dual Coxeter numbers of the respective symmetry algebras.

arXiv comment51 pages, 7 figures

References in corpus (18)

• On integrability of the Yang-Baxter $\si$-model
• Group theory factors for Feynman diagrams
• On classical q-deformations of integrable sigma-models
• Integrable interpolations: From exact CFTs to non-Abelian T-duals
• Integrability of the bi-Yang-Baxter sigma-model
• Supersymmetric Nonlinear Sigma Models as Gauge Theories
• GLSM's for partial flag manifolds
• The integrable harmonic map problem versus Ricci flow
• Integrable 2d sigma models: quantum corrections to geometry from RG flow
• The Character of Pure Spinors
• Gauge Theory And Integrability, III
• Complex structures and zero-curvature equations for sigma-models
• Sigma models as Gross-Neveu models
• Quantum flag manifold $\sigma$-models and Hermitian Ricci flow
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• On loop corrections to integrable $2D$ sigma model backgrounds
• Curved Beta-Gamma Systems and Quantum Koszul Resolution
• Integrable sigma models on Riemann surfaces

Cited by in corpus (3)

• Two-Loop Turbulent Helical Magnetohydrodynamics: Large-Scale Dynamo and Energy Spectrum
• Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism
• On First-Order GLSM for Sigma Models