Mirror Symmetry in 2+1 and 1+1 Dimensions

Details Mirror Symmetry in 2+1 and 1+1 Dimensions Mirror Symmetry in 2+1 and 1+1 Dimensions

2001-05-08

arxiv.org/abs/hep-th/0105075v1

JHEP 0107:022,2001

Physics

High Energy Physics

High Energy Physics - Theory

30 pages, 1 figure

Scientific paper

10.1088/1126-6708/2001/07/022

We study the Coulomb-Higgs duality of N=2 supersymmetric Abelian Chern-Simons theories in 2+1 dimensions, by compactifying dual pairs on a circle of radius R and comparing the resulting N=(2,2) theories in 1+1 dimensions. Below the compactification scale, the theory on the Higgs branch reduces to the non-linear sigma model on a toric manifold. In the dual theory on the Coulomb branch, the Kaluza-Klein modes generate an infinite tower of contributions to the superpotential. After resummation, in the limit R->0 the superpotential becomes that of the Landau-Ginzburg model which is the two-dimensional mirror of the toric sigma model. We further examine the conjecture of all-scale three-dimensional mirror symmetry and observe that it is consistent with mirror symmetry in 1+1 dimensions.

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