No abstract

We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schomerus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps towards computing superpotentials on the D-brane world-volumes.

We define the concept of Π-stability, a generalization of µ-stability of vector bundles, and argue that it characterizes N = 1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N = 2 supersymmetry in four dimensions.

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.

We study the D-brane spectrum on a two-parameter Calabi-Yau model. The analysis is based on different tools in distinct regions of the moduli space: wrapped brane configurations on elliptic fibrations near the large radius limit, and SCFT boundary states at the Gepner point. We develop an explicit correspondence between these two classes of objects, suggesting that boundary states are natural quantum generalizations of bundles. We also find interesting D-brane dynamics in deep stringy regimes. The most striking example is, perhaps, that nonsupersymmetric D6-D0 and D4-D2 large radius configurations become stable BPS states at the Gepner point.