Equivalences between GIT quotients of Landau-Ginzburg B-models
Algebraic Geometry
2011-05-09 v3 High Energy Physics - Theory
Abstract
We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of Landau-Ginzburg B-models that arise as different GIT quotients of a vector space by a one-dimensional torus, and show that for each such pair the two categories of B-branes are quasi-equivalent. In fact we produce a whole set of quasi-equivalences indexed by the integers, and show that the resulting auto-equivalences are all spherical twists.
Cite
@article{arxiv.0910.5534,
title = {Equivalences between GIT quotients of Landau-Ginzburg B-models},
author = {Ed Segal},
journal= {arXiv preprint arXiv:0910.5534},
year = {2011}
}
Comments
v3: Added two references. Final version, to appear in Comm. Math. Phys