Mirror symmetry in 2+1 and 1+1 dimensions

Citation
M. Aganagic et al., Mirror symmetry in 2+1 and 1+1 dimensions, J HIGH EN P, 2001(7), 2001, pp. NIL_487-NIL_516
Citations number
31
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Physics
Journal title
JOURNAL OF HIGH ENERGY PHYSICS
ISSN journal
1029-8479 → ACNP
Volume
2001
Issue
7
Year of publication
2001
Pages
NIL_487 - NIL_516
Database
ISI
SICI code
1029-8479(200107)2001:7<NIL_487:MSI2A1>2.0.ZU;2-V
Abstract
We study the Coulomb-Higgs duality of N = 2 supersymmetric abelian Chern-Si mons 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 dimensi ons. Below the compactification scale, the theory on the Higgs branch reduc es 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 c ontributions 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 con jecture of all-scale three-dimensional mirror symmetry and observe that it is consistent with mirror symmetry in 1 + 1 dimensions.