T-dualities in gauged linear sigma models

We describe non-Abelian T-dualities for N = 2 two dimensional gauged linear sigma model (GLSM). We start with the case of left and right (2, 2) supersymmetry (SUSY), U (1) gauge group, and global non-Abelian symmetries. Our analysis applies to the specialization of the GLSM with the global group SU (2) SU (2), 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 U (1) gauge field, and discuss the coincident singularity at the conifold point. We further present the non-Abelian T-dualization of models with (0, 2) SUSY, analyzing the case of global symmetry SU (2). In this case the full non-Abelian duality can be solved. The dual geometries with and without non-perturbative corrections to the superpotential coincide. The structure of the dual non-perturbative corrections employed are determined based on symmetry arguments. The non-Abelian T-dualities reviewed here lead to potential new symmetries between physical theories.