Transforming Calabi-Yau Constructions: Generating New Calabi-Yau Manifolds with Transformers

The vastness of the string landscape presents a serious computational challenge. This immensity stems from the multitude of choices for the internal manifolds on which string theory is compactified (or for non-geometric constructions, choices of conformal field theory). Even with a fixed compactification manifold, additional discrete choices--such as bundle or brane configurations, and the quantized fluxes threaded through internal cycles--further enlarge the space of solutions. Despite its vastness, the string landscape is conjectured to be finite, in the sense that there are only finitely many low energy effective field theories with a fixed, finite energy cutoff that are consistent with quantum gravity [1-3]. The finiteness of the landscape is both an important premise in the program of landscape statistics [1] and argued to be a universal property of quantum gravity [2]. It is however only when we restrict to very small regions of the landscape, e.g., intersecting D-brane models in a specific Calabi-Yau orientifold, that an exact number of solutions is known [4] (though it was shown earlier that the number is finite [5]). Compactifications of string theory on Calabi-Yau manifolds stand out as an especially well-motivated class of solutions for data mining the landscape. In particular, Calabi-Yau threefolds yield four-dimensional vacuum configurations of superstring theory that can potentially accommodate realistic particle physics coupled to gravity [6].