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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-Abelianglobal symmetry SU(2)xSU(2). A non-Abelian T-duality can be constructed whichcan be described by gauging the global non-Abelian symmetry. This leads to adual action, in terms of the dual model Kaehler and superpotential terms, whichinclude twisted chiral superfields dependence. Comparing the effectivepotentials for the U(1) fields on the original and the dual models we determinethe instanton corrections to the dual action. We obtain the supersymmetry vacuasolution of the dual model, in three cases: first in an Abelian directioninside SU(2)xSU(2), then for an Abelian direction considering instantoncorrections and finally for a semi-chiral non Abelian vector superfield. Thedual geometry for all of these cases (SUSY vacua space) is given by T5xR.However the instanton corrections restrict the Fayet-Iliopoulos term to be zeroand fix the theta-term, which implies that the duality is established for thecase of the singular conifold. We also discuss the U(1)A R-symmetry in the dualmodel and its possible role.

Non Abelian dual of the resolved conifold gauged linear sigma model