Würzburg Seminar on Quantum Field Theory and Gravity

We explore T-dualities between two-dimensional gauged linear sigma models (GLSMs). The supersymmetric vacua space of GLSMs represents string theory geometries; in the infrared the GLSM flows to string theory with these vacua as target space. The GLSMs considered have U(1) gauge group and (2,2) or (0,2) supersymmetries, with non-Abelian global symmetries. T-duality is realized by gauging global symmetries and adding Lagrange multipliers. Integration of the gauged fields yields the dual model, whereas integration of the Lagrange multipliers leads to the original model. Notable examples include Abelian T-duals of Hori and Vafa, leading to mirror symmetry. We implement non-Abelian T-duality, encompassing non-perturbative corrections, deriving duals for models with SU(2) and SU(2)xSU(2) global symmetry. As mirror symmetry, these dualities could relate string theories on distinct geometries.