Rank-2 attractors and Deligne’s conjecture

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 develop methods to analyze algebraic de Rham cohomologies and illustrate how our work by focusing on an example in a recent paper Candelas, la Ossa, Elmi van Straten. look at connections between attractors string theory Deligne's conjecture special values $L$-functions. also formulate several open questions concerning potential number theory.