Topological D-Branes and Commutative Algebra

Abstract

We show that questions concerning the topological B-model on a Calabi-Yau manifold in the Landau-Ginzburg phase can be rephrased in the language of commutative algebra. This yields interesting and very practical methods for analyzing the model. We demonstrate how the relevant "Ext" groups and superpotentials can be computed efficiently by computer algebra packages such as Macaulay. This picture leads us to conjecture a general description of D-branes in linear sigma models in terms of triangulated categories. Each phase of the linear sigma model is associated with a different presentation of the category of D-branes.

25 pages, refs added

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Cited by in corpus (8)

• D-brane superpotentials and RG flows on the quintic
• Decompactifications and Massless D-Branes in Hybrid Models
• Moduli Webs and Superpotentials for Five-Branes
• D-Branes in Topological String Theory
• Remarks on quiver gauge theories from open topological string theory
• Triangle-generation in topological D-brane categories
• Orientifolds and D-branes in N=2 gauged linear sigma models
• On the Correspondence of Open and Closed Strings