Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
D-Branes on Calabi-Yau Manifolds
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abstract
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.
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An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
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Hodge Loci and Complex Multiplication via Generalized Symmetries in Calabi-Yau sigma models
Proposes a CFT analogue of Hodge loci in Calabi-Yau sigma models via non-trivial TDL categories of topological defects, with CM number field embeddings at special points for elliptic curves and K3 surfaces.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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All the D-Branes of Resurgence
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