A team led by experts in string theory Burt Ovrut from the University of Pennsylvania and Andre Lukas from Oxford took a step further. They utilized Ruehle’s software for calculating metrics, which Lukas had a hand in developing. Expanding on this foundation, they incorporated 11 neural networks to manage various types of characteristics. These networks enabled them to compute a range of fields with more diverse shapes, creating a more realistic environment that cannot be explored using other methods. These machines learned the metric and field arrangements, calculated the Yukawa couplings, and determined the masses of three types of quarks across six differently shaped Calabi-Yau manifolds. Anderson commented, “This is the most accurate calculation of its kind that has ever been achieved.”
While none of these Calabi-Yau manifolds correspond to our universe due to the identical masses of two quarks, the six variations in our world exhibit three tiers of masses. Nevertheless, these results demonstrate that machine learning algorithms can guide physicists from a Calabi-Yau manifold to specific particle masses.
“Until now, such calculations would have been unimaginable,” mentioned Constantin, a team member based at Oxford.
Numbers Game
The neural networks encounter challenges with doughnuts having more than a few holes, and researchers aim to investigate manifolds with hundreds of holes in the future. The researchers have only examined relatively simple quantum fields so far. Ashmore suggested that a more advanced neural network might be required to reach the standard model.
The quest to find particle physics within the solutions of string theory is a numbers game. The more diverse doughnuts you analyze, the higher the chances of finding a match. String theorists can now compare doughnuts with reality after numerous years of effort. However, even the most optimistic theorists acknowledge the slim probability of discovering a match by sheer luck. The number of Calabi-Yau doughnuts alone could be infinite. Ruehle stated, “You have to figure out how to manipulate the system.”
One strategy is to examine thousands of Calabi-Yau manifolds and search for patterns that could guide the search. By manipulating the manifolds in different ways, physicists might develop an intuitive understanding of the shapes that result in specific particles. Ashmore expressed hope that by analyzing specific models, they might inadvertently come across the correct model for our universe.
Lukas and his team at Oxford plan to embark on this exploration, experimenting with their most promising doughnuts and adjusting the characteristics as they strive to identify a manifold that generates a realistic distribution of quarks. Constantin believes they will identify a manifold reproducing the masses of the remaining known particles within a few years.
“To make it interesting, there should be some new physical predictions.”
Renate Loll, Professor in Theoretical Physics, Radboud University, the Netherlands
On the other hand, some string theorists believe it is premature to closely examine individual manifolds. Thomas Van Riet from KU Leuven is a string theorist involved in the “swampland” research program, which aims to identify common features among all mathematically consistent string theory solutions. He and his colleagues aim to eliminate broad categories of string solutions before delving into specific doughnuts and characteristics.
“It’s beneficial that researchers are utilizing machine learning, as it will likely be necessary at some point,” Van Riet stated. However, he emphasized the importance of understanding underlying principles and patterns before focusing on specific details.
