Phases Of N=2 Theories In 1+1 Dimensions With Boundary

Details Phases Of N=2 Theories In 1+1 Dimensions With Boundary Phases Of N=2 Theories In 1+1 Dimensions With Boundary

2008-03-14

arxiv.org/abs/0803.2045v1

Physics

High Energy Physics

High Energy Physics - Theory

265 pages

Scientific paper

We study B-type D-branes in linear sigma models with Abelian gauge groups. The most important finding is the grade restriction rule. It classifies representations of the gauge group on the Chan-Paton factor, which can be used to define a family of D-branes over a region of the K\"ahler moduli space that connects special points of different character. As an application, we find a precise, transparent relation between D-branes in various geometric phases as well as free orbifold and Landau-Ginzburg points. The result reproduces and unifies many of the earlier mathematical results on equivalences of D-brane categories, including the McKay correspondence and Orlov's construction.

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