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

TL;DR

This paper reformulates the $ ext{CP}^{n-1}$ sigma model with fermions as a gauged Gross-Neveu model, revealing its supersymplectic structure and analyzing gauge anomalies through phase space properties.

Contribution

It introduces a novel formulation of the $ ext{CP}^{n-1}$ model with fermions as a gauged Gross-Neveu model, connecting supersymplectic geometry with gauge anomaly analysis.

Findings

Identification of the super phase space as a supersymplectic quotient.

Demonstration that gauge anomalies involve contributions from both bosons and fermions.

Establishment of the worldsheet supersymmetric model as a supersymplectic quotient.

Abstract

We elaborate the formulation of the $\mathsf{CP^{n-1}}$ 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.