The spectrum of BPS branes on a noncompact Calabi-Yau

Abstract

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O IP 2 (−3), a Calabi-Yau ALE space asymptotic to C 3 /Z 3 . We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.

Defects and D-brane monodromies

“…The corresponding large volume complex can be read off from (4.43) to be 46) giving rise to the expected Fourier-Mukai kernel…”

Matrix Factorizations, D-branes and their deformations

“…We cannot decide within the topological sector whether a composite is stable in the underlying physical theory: this depends on whether the charge of Ψ is less than one or not, i.e., whether Ψ is a relevant operator or not in the physical theory. Stability of a composite is indeed a complicated concept due its dependence on the Kähler moduli [70,71]. Namely, in some region of the Kähler moduli space the formation of the composite is energetically favorable and the coupling T acquires a non-zero (Kähler moduli dependent) vacuum expectation value there.…”

D-branes on Calabi–Yau Manifolds and Superpotentials

“…But we can describe salient pieces. We start now from a multiple Actually, for quiver without relations we could have resorted to the more handy Hom complex provided by Kac [30] (for a review see [15]). So the method comes into its own for the case with relations.…”

“…In particular, one can check that for the Beilinson quiver the standard complex can be simplified to yield the simpler procedure considered in [15].…”

“…In [15,12] it was found that these boundary states could be largely understood in terms of a standard construction of sheaves on projective space IP n formulated by Beilinson [3].…”