T-dualities in gauged linear sigma models

In this paper, we describe non-Abelian T-dualities for a two-dimensional (2D) gauged linear sigma model (GLSM) with [Formula: see text] supersymmetry (SUSY). We start with the case of left and right SUSY [Formula: see text], [Formula: see text] gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group [Formula: see text], whose original model is the resolved conifold. We analyze the dual model and compute the periods on the dual geometry, matching the effective potential for the [Formula: see text] gauge field, and discussing the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with [Formula: see text] SUSY, analyzing the case of global symmetry [Formula: see text]. In this case, the full non-Abelian duality can be solved. The dual geometries with and without nonperturbative corrections to the superpotential coincide. The structure of the dual nonperturbative corrections is determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories.