On First-Order GLSM for Sigma Models

TL;DR

This paper reviews recent advances in first-order GLSM (Gross-Neveu formalism) for sigma models, detailing the construction framework and classifying models equivalent to sigma models on certain Hermitian spaces.

Contribution

It introduces a general first-order GLSM construction method and characterizes when generalized Gross-Neveu models are equivalent to specific sigma models.

Findings

Provides a construction framework for first-order GLSMs.

Classifies models equivalent to sigma models on Hermitian spaces.

Uses $ ext{CP}^{n-1}$ as a fundamental example.

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.