A group led by string theory veterans Burt Owrut from the University of Pennsylvania and Second Luke Oxford went further. They, too, started with Ruehle metric software, which Lukas helped develop. Building on this foundation, they added a series of 11 neural networks to handle different types of sprinkles. These networks allowed them to calculate an assortment of fields that can take on a richer variety of shapes, creating a more realistic setting that cannot be explored with any other technique. This army of machines learned the metric and field layout, calculated the Yukawa couplings and spit it out masses of three types of quarks. It did all this for six differently shaped Calabi-Yau splitters. “This is the first time anyone has been able to calculate them with such accuracy,” Anderson said.
None of these Calabi-Yaus underlie our universe, because two of the quarks have identical masses, while the six varieties in our world have three levels of masses. Rather, the results provide proof that machine learning algorithms can guide physicists from Calabi-Yau manifolds down to specific particle masses.
“Until now, any calculations of this type would have been unthinkable,” said Constantin, a member of the Oxford group.
Numbers game
Neural networks choke on buds with more than a few holes, and researchers would eventually like to study manifolds with hundreds. So far, researchers have only studied rather basic quantum fields. To move to the standard model, Ashmore said, “you may need a more sophisticated neural network.”
Greater challenges appear on the horizon. Trying to find our particle physics in string theory solutions – if there even is one – is a numbers game. The more sprinkled donuts you can check, the more likely you are to find a match. After decades of effort, string theorists can finally check the bullshit and compare it to reality: the observed masses and couplings of elementary particles. However, even the most confident theorists admit that the chances of finding a partner through blind luck are extremely low. The number of Calabi-Yau buds alone could be infinite. “You have to learn to play the system,” Ruehle said.
One way is to look at thousands of Calabi-Yau manifolds and try to spot any patterns that could guide the search. For example, by stretching and compressing manifolds in different ways, physicists can develop an intuitive sense of what shapes lead to what particles. “What you really hope is that after you look at specific models, you’ll have a solid foundation of reasoning,” Ashmore said, “and you’ll come across the right model for our world.”
Lukas and his colleagues at Oxford plan to begin this research by poking their most promising donuts and playing with sprinkles, trying to find a manifold that will produce a realistic population of quarks. Constantin believes that within a few years they will find a manifold that reproduces the masses of the remaining known particles.
Other string theorists, however, believe that it is premature to begin examining individual manifolds. Thomas Van Riet from KU Leuven is a string theorist focusing on “swamp” research program.which aims to identify features common to all mathematically consistent solutions of string theory – such as extreme weakening of gravity in relation to other forces. He and his colleagues want to rule out a wide range of string solutions – or possible universes – before they even start thinking about specific donuts and sprinkles.
“It’s good that people are doing machine learning because I’m sure we’re going to need it at some point,” Van Riet said. But first, “we need to think about basic principles, patterns. They ask for details.”