D-brane Categories for Orientifolds -- The Landau-Ginzburg Case

TL;DR

This paper develops a framework for classifying D-branes in orientifold Landau-Ginzburg models, extending topological correlator formulas to unoriented cases and orbifolds, with implications for string theory constructions.

Contribution

It introduces a classification scheme for D-branes in orientifold Landau-Ginzburg models, including consistency conditions and extended correlator formulas, advancing the understanding of orientifold string theories.

Findings

Classification of D-branes in orientifold Landau-Ginzburg models

Generalized topological correlator formulas for unoriented worldsheets

Discovery of doubled Knörrer periodicity in orientifold context

Abstract

We construct and classify categories of D-branes in orientifolds based on Landau-Ginzburg models and their orbifolds. Consistency of the worldsheet parity action on the matrix factorizations plays the key role. This provides all the requisite data for an orientifold construction after embedding in string theory. One of our main results is a computation of topological field theory correlators on unoriented worldsheets, generalizing the formulas of Vafa and Kapustin-Li for oriented worldsheets, as well as the extension of these results to orbifolds. We also find a doubling of Knoerrer periodicity in the orientifold context.