D-Branes on Calabi-Yau Manifolds
By P. Aspinwall. 2004
291 citations recorded by the source corpus.
In this review we study BPS D-branes on Calabi-Yau threefolds. Such D-branes naturally divide into two sets called A-branes and B-branes which are most easily understood from topological field theory. The main aim of this paper is to provide a self-contained guide to the derived category approach to B-branes and the idea of Pi-stability. We argue that this mathematical machinery is hard to avoid for a proper understanding of B-branes. A-branes and B-branes are related in a very complicated and interesting way which ties in with the ``homological mirror symmetry'' conjecture of Kontsevich. We motivate and exploit this form of mirror symmetry. The examples of the quintic 3-fold, flops and orbifolds are discussed at some length. In the latter case we describe the role of McKay quivers in the context of D-branes. These notes are to be submitted to the proceedings of TASI03.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/801eac0b07496346e0f1f0edf2c51c0bedc48afd
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
In Nuclear and High Energy Physics
Citations in the corpus
- Brane tilings and their applications (2008, background): “We also have many mathematics introductions [230–233] and physics reviews [224,225].”
- Moduli Stabilisation versus Chirality for MSSM like Type IIB Orientifolds (2007, background): “The chiral massless spectrum arising from open strings stretched between two D7-branes wrapping two four-cycles Da and Db and carrying gauge bundles Va and Vb is determined by [39, 40] Iab = ∫”
- Phases Of N=2 Theories In 1+1 Dimensions With Boundary (2008, background): “In particular, the D-brane V in our Example (A) confirms the results from the mirror computation of the central charge in [76].”
- Khovanov-Rozansky Homology and Topological Strings (2004, background): “Furthermore, this category has a triangulated structure, which plays an important role in the notion of D-brane stability, see [26] for a recent review.”
- D-brane Deconstructions in IIB Orientifolds (2008, background): “In particular the cosmological constant can in princi- ple be discretely tuned to become extremely small, easily of the order of the measured cosmological constant or less [6, 7].”
- Stability Manifold of P^1 (2004, background): “Douglas’s work on Π-stability of D-branes [8], [9], and [10].”
- D-instantons and twistors (2008, background): “In the large volume limit, their classical action is given by [66, 67, 62]”
- On stability conditions for the quintic threefold (2018, background): “2,whenμ ∈ [2, 10],we only need the following weaker but neat bound.”