Abstract
In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.
Highlights
As is well known, gauged linear sigma models exhibit different phases for different ranges of the Fayet-Iliopoulos parameter r associated to the U(1) gauge group [1]
Results on the anomalous “non-Calabi-Yau” case appeared more recently in [3, 4]. The authors of these papers obtain a prescription of the D-brane transport on the level of individual D-branes: starting in one phase, a D-brane is first lifted to the gauged linear sigma model
With the exception of the truncation, which we introduced in an ad-hoc fashion to obtain RG defects from the gauged linear sigma models (GLSMs) identity defect, and which probably has its origins in stability considerations, there were no choices involved in our construction
Summary
Phases in which the gauge group is completely broken and all modes transverse to {U = 0} are massive are called geometric phases In these phases, the Higgs branch is effectively described by a non-linear sigma model with target space {U = 0}/U(1)k. If on the other hand the space of vacua {U = 0}/U(1)k consists of a single point and all modes transverse to the orbit of the complexified gauge group remain massless, the Higgs branch is effectively described by a Landau-Ginzburg (orbifold) theory. But in contrast to the IR phase, it is a pure Higgs phase, i.e. it does not have additional Coulomb vacua
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