Branes in hearts with perverse sheaves
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Various topological properties of D-branes in the type--IIA theory are captured by the topologically twisted B-model, treating D-branes as objects in the bounded derived category of coherent sheaves on the compact part of the target space. The set of basic D-branes wrapped on the homology cycles of the compact space are taken to reside in the heart of t-structures of the derived category of coherent sheaves on the space at any point in the Kähler moduli space. The stability data entails specifying a t-structure along with a grade for sorting the branes. Considering an example of a degenerate Calabi-Yau space, obtained via geometric engineering, that retains but a projective curve as the sole non-compact part, we identify the regions in the Kähler moduli space of the curve that pertain to the different t-structures of the bounded derived category of coherent sheaves on the curve corresponding to the different phases of the topological branes.
21 pages, LaTeX, references added, cosmetic changes
21 pages, LaTeX, references added, cosmetic changes