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Categories of massless D-branes and del Pezzo surfaces

  • Nicolas AddingtonEmail author
  • Paul S. Aspinwall
Article

Abstract

In analogy with the physical concept of a massless D-brane, we define a notion of “\( \mathbb{Q}\hbox{-}\mathrm{masslessness} \)” for objects in the derived category. This is defined in terms of monodromy around singularities in the stringy Kähler moduli space and is relatively easy to study using “spherical functors”. We consider several examples in which del Pezzo surfaces and other rational surfaces in Calabi-Yau threefolds are contracted. For precisely the del Pezzo surfaces that can be written as hypersurfaces in weighted \( {{\mathbb{P}}^3} \), the category of \( \mathbb{Q}\hbox{-}\mathrm{massless} \) objects is a “fractional Calabi-Yau” category of graded matrix factorizations.

Keywords

D-branes Differential and Algebraic Geometry 

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Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  1. 1.Department of MathematicsBox 90320, Duke UniversityDurhamU.S.A.

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