Examining the string landscape using data science and network techniques

Abstract

The largest known database of Calabi-Yau threefolds was produced by Kreuzer and Skarke, who explicitly constructed all 473,800,776 reflexive polytopes in four dimensions. From these polyhedra, one can construct ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. Due to the discrete nature of lattice polytopes, thesepolytopes and their resulting threefolds are particularly amenable to computational analysis. We first examine Z2 divisor exchange involutions in these threefolds, and present an algorithm for locating and classifying their orientifold planes using the toric data, as well as the results of applying this algorithm to the Calabi-Yau geometries explicitly constructed in [3]. Next, we use network science as a tool for studying vacuum selection in the string landscape, by constructing a network of vacua whose edges represent topological transitions and examining the late-time behaviour under a standard bubble cosmology. The resulting nontrivial probability distribution suggests a possible mechanism for vacuum selection in string theory. Then, we attempt to give an upper bound on the number of possible threefolds arising from this set by estimating the number of fine, regular, star triangulations. The estimate is performed using an equation learner neural network, which yields an estimate nFRST = 1.465 × 1010,505 . A similar analysis is performed on the reflexive polytopes in three dimensions as a test of this method. Finally, we examine an extension of the toric Swiss cheese algorithm proposed in [4], in which an initial GLk (Z) rotation is applied to the toric divisors. The results of this scan lead to an additional 4,347 Swiss cheese solutions with h1,1 (X) ≤ 6 in the Kreuzer-Skarke dataset.