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\(D\)-brane categories for orientifolds-the Landau-Ginzburg case. (English) Zbl 1246.81337

Summary: 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 Knörrer periodicity in the orientifold context.

MSC:

81T45 Topological field theories in quantum mechanics
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
18E30 Derived categories, triangulated categories (MSC2010)
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