Non Abelian dual of the resolved conifold gauged linear sigma model

We consider a U(1) Gauged Linear Sigma Model (GLSM) with (2,2) supersymmetry, leading to a susy vacua of the resolved conifold. It possesses the non-Abelian global symmetry SU(2)xSU(2). A non-Abelian T-duality can be constructed which can be described by gauging the global non-Abelian symmetry. This leads to a dual action, in terms of the dual model Kaehler and superpotential terms, which include twisted chiral superfields dependence. Comparing the effective potentials for the U(1) fields on the original and the dual models we determine the instanton corrections to the dual action. We obtain the supersymmetry vacua solution of the dual model, in three cases: first in an Abelian direction inside SU(2)xSU(2), then for an Abelian direction considering instanton corrections and finally for a semi-chiral non Abelian vector superfield. The dual geometry for all of these cases (SUSY vacua space) is given by T5xR. However the instanton corrections restrict the Fayet-Iliopoulos term to be zero and fix the theta-term, which implies that the duality is established for the case of the singular conifold. We also discuss the U(1)A R-symmetry in the dual model and its possible role.