This project focuses on string theory, a leading candidate for unifying particle physics with gravity. The proposal aims to characterize features of the typical string compactification by applying algebraic geometry to study topological invariants of manifolds and to search for correlations between these data and structures relevant to model building, both in particle physics and cosmology.
This research is of interest to an interdisciplinary community of theoretical physicists, mathematicians and computer scientists. Researchers in this project are highly involved with the NSF-sponsored String Vacuum Project the results of this research are expected to cross-fertilize that endeavor. The software employed for computational algebraic geometry is publicly available, and the project involves several algorithmic improvements that can be incorporated into future versions of these codes. All computations are to be ported and developed for use in the Microsoft Azure platform.
This award corresponds to the Computing in the Cloud competition and is co-funded by the Office of Multidisciplinary Activities of the Directorate of Mathematical and Physical Sciences.
The basic research goals of the work supported by this award involve the study of superstring theory and elementary particle physics. The PI, together with a team of senior personnel, focused on topics which are amenable to a large-scale computational approach. All of these subjects involve studying a particular type of six-dimensional surface known as a Calabi-Yau three-fold. When string theory is compactified on such surfaces, the resulting four-dimensional physics is known to possess supersymmetry, and may yield a theory of particle physics that is similar to (and perhaps identical to) the Standard Model of particle physics we observe experimentally. More specifically, the topics studied included (1) the construction of Calabi-Yau three-folds from reflexive polytopes, and the enumeration of their topological properties, (2) the search for semi-realistic models in heterotic string theory via the construction of line bundles on Calab-Yau three-folds, (3) the construction and study of more general vector bundles on Calami-Yau three-folds, and (4) the study of the vacuum moduli spaces of gauge-theories (like the supersymmetric version of the Standard Model itself), in an effort to `reverse engineer’ the Standard Model for treatment by string theorists. The scale of the problems attacked is large. For example, the number of reflexive polytopes from which Calabi-Yau three-folds can be constructed is over 500 million. Each such polytope generally produces more than one Calabi-Yau manifold. In the study of heterotic-string theory, over 1040 vector bundles were constructed, resulting in 35,000 grand-unified theories that can now be studied by phenomenologists. In addition to the specific physics problems that were addressed using this award, the work that was supported has had broader impacts in a number of areas. Our research efforts have involved inter-disciplinary collaborations with mathematicians and algebraic geometers, both symbolic and numerical, which has built new bridges between our communities. Indeed, this work has been presented at the Algebric Geometry section of meetings of the Society of Industrial and Applied Mathematics. Furthermore, the computational tools we have developed were improvements on pre-existing software, and have been made available to the public. So too, the main end result --- a searchable database of topological data for over 100,000 Calabi-Yau three-folds --- is now hosted on a public website, where many research groups are already taking advantage of the work we have done to further their own research efforts. This has had immense value for the field, and could not have been accomplished by any one individual or single group, but required the collaborative efforts of our team, and the large amount of computing resources made available by Microsoft for the purpose of this grant.
