The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look

Abstract

We elaborate the formulation of the $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$ sigma model with fermions as a gauged Gross-Neveu model. This approach allows to identify the super phase space of the model as a supersymplectic quotient. Potential chiral gauge anomalies are shown to receive contributions from bosons and fermions alike and are related to properties of this phase space. Along the way we demonstrate that the worldsheet supersymmetric model is a supersymplectic quotient of a model with target space supersymmetry. Possible generalizations to other quiver supervarieties are briefly discussed.

29 pages, 2 figures

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• An elliptic integrable deformation of the Principal Chiral Model
• Monopole harmonics on ${\mathbb{CP}}^{n-1}$
• Integrable sigma models on Riemann surfaces
• Grassmannian Sigma Models
• Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism
• $\beta$-function of the level-zero Gross-Neveu model
• On First-Order GLSM for Sigma Models