D-branes in Toroidal Orbifolds and Mirror Symmetry

TL;DR

This paper analyzes D-branes in T^2/Z_4 orbifolds using mirror symmetry, describing them via boundary states and matrix factorizations, and provides a geometric interpretation as D1-branes at fixed points.

Contribution

It introduces a method to describe D-branes in toroidal orbifolds through mirror symmetry, boundary states, and matrix factorizations, with a geometric interpretation.

Findings

Identification of a minimal set of branes

Explicit construction of boundary states

Geometric interpretation as D1-branes at fixed points

Abstract

We study D-branes extended in T^2/Z_4 using the mirror description as a tensor product of minimal models. We describe branes in the mirror both as boundary states in minimal models and as matrix factorizations in the corresponding Landau-Ginzburg model. We isolate a minimal set of branes and give a geometric interpretation of these as D1-branes constrained to the orbifold fixed points. This picture is supported both by spacetime arguments and by the explicit construction of the boundary states, adapting the known results for rational boundary states in the minimal models. Similar techniques apply to a larger class of toroidal orbifolds.