On gauged linear sigma models with torsion

Abstract: We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chi-ral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kähler, hy-perkähler, and Calabi-Yau manifolds. The (2, 2) supersymmetry guarantees that these spaces are generalized Kähler. Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kähler structure on the conifold.