Introduction to Gauged Linear Sigma Models

Gauge Linear Sigma Models (GLSMs) are certain class of two-dimensional supersymmetric gauge theories whose low energy dynamics are dictated by the choice of physical parameters of the model (coupling constants). For a given GLSM depending on the values of these parameters they can be described (at low energies) by a nonlinear sigma model (NLSM) whose target space is Calabi-Yau, or a Landau-Ginzburg model or other types of supersymmetric theories. These are known as the “phases” of the GLSM. We will review the pioneering work of Witten for the construction of GLSMs with at least one geometric phase and how they can be used to describe different classes of Calabi-Yau threefolds, such as complete intersections as well as more general ones of determinantal type.