B-type D-branes in hybrid models

TL;DR

This paper investigates B-type D-branes in hybrid models, which are fibrations of Landau-Ginzburg orbifolds over geometric bases, establishing their mathematical structure, compatibility conditions, and connections to geometric branes via GLSM techniques.

Contribution

It characterizes B-type D-branes in hybrid models using matrix factorizations and geometric data, and links these to geometric branes through GLSM methods.

Findings

D-branes are described by matrix factorizations in the fiber.

Compatibility conditions with orbifold actions and R-symmetry are derived.

Explicit examples of hybrid B-branes in Calabi-Yau models are constructed.

Abstract

A hybrid model is a fibration of a Landau-Ginzburg orbifold over a geometric base. We study B-type D-branes in hybrid models. Imposing B-type supersymmetry on the boundary action, we show that D-branes are specified by matrix factorisations in the fibre direction, together with some geometric data associated to the base. We also deduce conditions for the compatibility of these branes with the bulk orbifold actions and R-symmetry. We construct examples of hybrid B-branes which are generalisations of well-studied branes in geometric and Landau-Ginzburg models. Hybrid models can arise at limiting points of the stringy Kahler moduli space of Calabi-Yaus, and can be realised as phases of the corresponding gauged linear sigma models (GLSMs). Using GLSM techniques, we establish connections between geometric branes and hybrid branes. As explicit examples, we consider one- and two-parameter Calabi-Yau hybrids with a $\mathbb{P}^1$-base.