Generating the superpotential on a D-brane category: I

Abstract

I study A-infinity enhancements of algebraic Calabi-Yau triangulated categories admitting a (triangle) generator, showing that the Serre pairing on such categories determines and is determined by a cyclic pairing on an enhancement of the generator. Using this result, I construct a formal topological string field action inducing an extended D-brane superpotential for such categories. I also give a procedure for lifting certain 2d boundary topological field theories to open topological string theories generated by a single D-brane.

84 pages, 2 figures

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Cited by in corpus (9)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Monads and comonads in module categories
• Matrix factorisations and open topological string theory
• D-brane Superpotentials: Geometric and Worldsheet Approaches
• Sheaves on local Calabi-Yau varieties
• Remarks on quiver gauge theories from open topological string theory
• Graded D-branes and skew-categories
• Triangle-generation in topological D-brane categories
• Constructing $A_{\infty }$-categories of matrix factorisations