Defects and phase transitions to geometric phases of abelian GLSMs

TL;DR

This paper studies gauged linear sigma models with U(1) gauge group, focusing on defects that connect different phases and act as functors between D-brane categories, providing explicit constructions in terms of matrix factorizations.

Contribution

It constructs explicit defects that transport D-branes between Landau-Ginzburg and geometric phases in abelian GLSMs, linking their D-brane categories.

Findings

Constructed defects implement phase transport of D-branes.

Defects induce functors between D-brane categories.

Explicit formulations in terms of matrix factorizations.

Abstract

We consider gauged linear sigma models with gauge group U(1) that exhibit a geometric as well as a Landau Ginzburg phase. We construct defects that implement the transport of D-branes from the Landau-Ginzburg phase to the geometric phase. Through their fusion with boundary conditions these defects in particular provide functors between the respective D-brane categories. The latter map (equivariant) matrix factorizations to coherent sheaves and can be formulated explicitly in terms of complexes of matrix factorizations.