Explore and exploit in the heterotic landscape

SNIC 2019/3-546


SNIC Medium Compute

Principal Investigator:

Magdalena Larfors


Uppsala universitet

Start Date:


End Date:


Primary Classification:

10301: Subatomic Physics

Secondary Classification:

10199: Other Mathematics




String theory is the leading candidate for a unification of gravity with particle physics. While its mathematical consistency makes it very interesting to study from an aesthetic point of view, it also comes with some caveats when trying to make actual real world predictions. The main one being, that it needs ten space time dimensions, rather than the four observable ones. The proposed solution to this problem is to take the total 10D space and write it as a direct product of flat 4D spacetime and some compact manifold. The shape of the compact manifold is related real physical observables and thus there are constraints on the type of manifolds being considered. For computational ease it is usual chosen to be a Calabi Yau manifold. While there have been about 473 million such manifolds constructed explicitly [Kreuzer:2000] the number of viable compactification configurations is magnitudes larger. Estimates of relevant configurations that need to be studied range from $10^{500}$ to $10^{272.000}$ [Ashok:2003, Halverson:2017, Taylor:2017]. The majority of these will not lead to realistic models, that is, consistent with our observable universe. The search for interesting models is optimistically described as looking for a needle in a haystack. It is obvious that string theory is in dire need of finding smart ways to explore its landscape. Recently, it has been proposed to use reinforcement learning agents to explore the string landscape [Halverson:2019]. Reinforcement learning, a branch of machine learning, has made major popular headlines by achieving super human performance in a variety of complex settings. Notably are the dominant wins against the world champion in GO, a board game with $\mathcal{O}(10^{170})$ possible board position, achieved by AlphaZero [Silver2017] and beating the current world champion in the computer game Dota2 [OpenAIfive 2019]. The algorithms were able to reinvent human strategies but also come up with new ones, previously unknown or deemed unfeasible by humans. These strong demonstrations makes it plausible that such algorithms also might find smart ways to explore the string landscape. In this project we aim to use the popular A3C agents [Mnih2016] to explore a corner of the heterotic landscape: compactifications on Complete Intersection Calabi Yau manifolds using sums of line bundles [Anderson:2012]. We have implemented two different environments for the agents to explore using the OpenAI gym package.