Rank-2 attractors and Deligne's conjecture

Abstract

In this paper, we will study the arithmetic geometry of rank-2 attractors, which are Calabi-Yau threefolds whose Hodge structures admit interesting splits. We will develop methods to analyze the algebraic de Rham cohomologies of rank-2 attractors, and we will illustrate how our methods work by focusing on an example in a recent paper by Candelas, de la Ossa, Elmi and van Straten. We will look at the interesting connections between rank-2 attractors in string theory and Deligne's conjecture on the special values of $L$-functions. We will also formulate several open questions concerning the potential connections between string theory and number theory.

arXiv comment19 pages. Several important changes. Correct the errors in early versions

References in corpus (5)

• N=2 Extremal Black Holes
• Supersymmetry and Attractors
• A One Parameter Family of Calabi-Yau Manifolds with Attractor Points of Rank Two
• Deligne's conjecture and mirror symmetry
• K3 mirror symmetry, Legendre family and Deligne's conjecture for Fermat quartic

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• Flux Vacua and Modularity for ${\mathbb{Z}}_2$ Symmetric Calabi-Yau Manifolds
• Classical Weight-Four L-value Ratios as Sums of Calabi--Yau Invariants