A group led by string theory veterans Burt Ovrut from the University of Pennsylvania and Andre Lucas of Oxford went further. They also started with Ruehle’s metric calculation software, which Lukas had helped develop. Building on that, they added a series of 11 neural networks to handle the different types of sparks. These networks allowed them to calculate a variety of fields that could take on a richer variety of shapes, creating a more realistic environment that cannot be studied with any other technique. This army of machines learned the metrics and layout of the fields, calculated the Yukawa couplings, and spat the masses of three types of quarks. He did all this for six Calabi-Yau collectors of different shapes. “This is the first time anyone has been able to calculate them with that degree of precision,” Anderson said.
None of those Calabi-Yaus is the basis of our universe, because two of the quarks have identical masses, while the six varieties of our world come in three mass levels. Rather, the results represent proof of principle that machine learning algorithms can take physicists from a Calabi-Yau manifold to specific particle masses.
“Until now, any such calculation would have been unthinkable,” said Constantin, a member of the Oxford-based group.
numbers game
Neural networks choke on donuts with more than a handful of holes, and researchers would eventually like to study varieties with hundreds. And so far researchers have only considered fairly simple quantum fields. To get up to the standard model, Ashmore said, “you may need a more sophisticated neural network.”
Greater challenges loom on the horizon. Trying to find our particle physics solutions to string theory (if there are any) is a numbers game. The more sprinkle-filled donuts you can check out, the more likely you are to find a match. After decades of effort, string theorists can finally check the rings and compare them to reality: the masses and couplings of the elementary particles we observe. But even the most optimistic theorists recognize that the chances of finding a partner by luck are cosmically low. The number of Calabi-Yau donuts alone can be infinite. “You have to learn to play the system,” Ruehle said.
One approach is to check thousands of Calabi-Yau collectors and try to discover any patterns that might guide the search. By stretching and squeezing the varieties in different ways, for example, physicists could develop an intuitive sense of which shapes lead to which particles. “What you’re really hoping for is to have sound reasoning after looking at particular models,” Ashmore said, “and finding the right model for our world.”
Lukas and his Oxford colleagues plan to begin that exploration, stimulating their most promising donuts and tinkering more with sparks as they try to find a variety that produces a realistic population of quarks. Constantin believes that in a matter of years they will find a variety that reproduces the masses of the rest of the known particles.
Other string theorists, however, think it is premature to begin examining individual varieties. Thomas Van Riet from KU Leuven is a string theorist who pursues Research program on “swamps”which seeks to identify characteristics shared by all mathematically consistent solutions of string theory, such as the extreme weakness of gravity in relation to the other forces. He and his colleagues aim to rule out wide swaths of string solutions (i.e. possible universes) before they even start thinking about specific donuts and sparks.
“It’s good that people are getting into this machine learning business, because I’m sure we’ll need it at some point,” Van Riet said. But first “we need to think about the underlying principles, the patterns. What they are asking are the details.”