Calabi-Yau Mirror Symmetry as a Gauge Theory Duality
arXiv:hep-th/9910184 · doi:10.1088/0264-9381/17/5/301
Abstract
We show that there are two different dualities of two dimensional gauge theories with N=(2,2) supersymmetry. One is basically a consequence of 3d mirror symmetry. The non-linear sigma model with Calabi-Yau target space on the Higgs branch of the gauge theory is mapped into an equivalent non-linear sigma model on the Coulomb branch of the dual theory, realizing a T-dual target space with torsion. The second duality is genuine to two dimensions. In addition to swapping Higgs and Coulomb branch it trades twisted for untwisted multiplets, implying a sign flip of the left moving U(1)_R charge. Succesive application of both dualities leads to geometric mirror symmetry for the target space Calabi-Yau.
10 pages