Spanning Class in the Category of Branes

Abstract

Given a generic anticanonical hypersurface $Y$ of a toric variety determined by a reflexive polytope, we define a line bundle $\mathcal{L}$ on $Y$ that generates a spanning class in the bounded derivative category $D^b(Y)$. From this fact, we deduce properties of some spaces of strings related with the brane $\mathcal{L}$. We prove a vanishing theorem for the vertex operators associated to strings stretching from branes of the form ${\mathcal{L}}^{\otimes i}$ to nonzero objects in $D^b(Y)$. We also define a gauge field on $\mathcal{L}$ which minimizes the corresponding Yang-Mills functional.

19 pages

References in corpus (2)

• Cohomological vertex operators
• Branes on $G$-manifolds

Cited by in corpus (1)

• Charge of $D$-branes on singular varieties