On First-Order GLSM for Sigma Models

Abstract

We review some recent developments in 1-st order GLSM construction, or so-called Gross-Neveu formalism for sigma models. We recall the general idea behind this framework and describe a 1-st order GLSM data from which the general generalized Gross-Neveu model can be constructed, using ${\mathbb{CP}}^{n-1}$ sigma model as simplest example. Then, we formulate a general statement that answers the question of which generalized Gross-Neveu models are equivalent to sigma models on compact homogeneous Hermitian spaces of classical groups endowed with the normal metrics.

8 pages. Prepared as a contribution to the conference "Supersymmetries and Quantum Symmetries 2024 (SQS'24)"

References in corpus (11)

• On First Order Formalism in String Theory
• Flag manifold sigma-models and nilpotent orbits
• Manifestly Covariant Worldline Actions from Coadjoint Orbits. Part I: Generalities and Vectorial Descriptions
• The $\mathsf{C}{\mathsf{P}}^{\mathsf{n}-1}$-model with fermions: a new look
• On loop corrections to integrable $2D$ sigma model backgrounds
• Integrable sigma models on Riemann surfaces
• Monopole harmonics on ${\mathbb{CP}}^{n-1}$
• Grassmannian Sigma Models
• Supersymmetric deformation of the ${\mathbb{CP}}^1$ model and its conformal limits
• Sigma models as Gross-Neveu models. II
• Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism