Calabi-Yau Mirror Symmetry as a Gauge Theory Duality

Details Calabi-Yau Mirror Symmetry as a Gauge Theory Duality Calabi-Yau Mirror Symmetry as a Gauge Theory Duality

1999-10-22

arxiv.org/abs/hep-th/9910184v1

Class.Quant.Grav.17:919-927,2000

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0264-9381/17/5/301

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.

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