Supersymmetric Grassmannian Sigma Models in Gross-Neveu Formalism

TL;DR

This paper reformulates supersymmetric Grassmannian sigma models using polynomial Lagrangians within the Gross-Neveu formalism, highlighting geometric and supersymmetric features, and providing new equivalent models for maximal isotropic cases.

Contribution

It introduces novel polynomial Lagrangian formulations for supersymmetric Grassmannian sigma models, making supersymmetry or geometry explicit, and extends the Gross-Neveu formalism to these models.

Findings

Reformulated models with polynomial interactions

Proposed two types of equivalent Lagrangians for maximal isotropic Grassmannians

Demonstrated models as current-current deformations of curved beta-gamma systems

Abstract

We revisit the classical aspects of $\mathcal{N}=(2,2)$ supersymmetric sigma models with Hermitian symmetric target spaces, using the so-called Gross-Neveu (first-order GLSM) formalism. We reformulate these models for complex Grassmannians in terms of simple supersymmetric Lagrangians with polynomial interactions. For maximal isotropic Grassmannians we propose two types of equivalent Lagrangians, which make either supersymmetry or the geometry of target space manifest. These reformulations can be seen as current-current deformations of curved $\beta \gamma$ systems. The $\mathsf{CP}^{1}$ supersymmetric sigma model is our prototypical example.