Physicists who have wandered the "landscape" of string theory - a space of billions and billions of mathematical solutions to a theory in which each solution provides the equations with which physicists try to describe reality - have stumbled upon a subset of such equations that include as many particles of matter as there are in our universe. However, this subset is huge: there are at least a quadrillion such solutions. This is the largest find in the history of string theory.
The universe in string theory
According to string theory, all particles and fundamental forces are generated by vibrating tiny strings. For mathematical consistency, these strings vibrate in 10-dimensional spacetime. And for consistency with our usual everyday experience of existence in the Universe, with three spatial and one time dimensions, the additional six dimensions are "compactified" so that they cannot be detected.
Different compactifications lead to different solutions. In string theory, “solution” refers to the vacuum of spacetime, which is governed by Einstein's theory of gravity combined with quantum field theory. Each solution describes a unique universe, with its own set of particles, fundamental forces, and other defining properties.
Some string theorists have focused their efforts on trying to find ways to relate string theory to the properties of our known observable universe - in particular, the Standard Model of particle physics, which describes all known particles and forces except gravity.
Much of this effort comes from a version of string theory in which strings interact weakly. Over the past twenty years, however, a new branch of string theory called F-theory has allowed physicists to work with strongly interacting - or tightly coupled - strings.
“The interesting results are that when the relationship is large, we can start to describe the theory very geometrically,” says Miriam Tsvetik of the University of Pennsylvania in Philadelphia.
Promotional video:
This means that string theorists can use algebraic geometry - which uses algebraic methods to solve geometric problems - to analyze different ways of compactifying extra dimensions in F theory and finding solutions. Mathematicians independently study some of the geometric shapes that appear in F-theory. “They provide us physicists with a wealth of tools,” says Ling Lin, also of the University of Pennsylvania. "Geometry is actually very important, it is the 'language' that makes F-theory a powerful structure."
Quadrillions of universes
And so Tsvetik, Lin, James Halverson of Northeastern University in Boston used these methods to identify a class of solutions with vibrating string modes that lead to the same spectrum of fermions (or matter particles) as described by the Standard Model - including the property, due to which fermions are of three generations (for example, electron, muon and tau are three generations of the same type of fermions).
The F-theory solutions discovered by Tsvetik and her colleagues also include particles that exhibit chirality (lack of symmetry about the right and left sides) of the Standard Model. In particle physics terminology, these solutions reproduce the exact "chiral spectrum" of particles in the Standard Model. For example, the quarks and leptons in these solutions have left and right versions, as in our universe.
The new work shows that there are at least a quadrillion solutions in which particles have the same chiral spectrum as in the Standard Model, 10 orders of magnitude more solutions than has been found in string theory so far. “This is by far the largest subclass of Standard Model solutions,” Tsvetik says. "What's amazing and nice is that it's all in tightly coupled string theory where geometry helps us."
Quadrillion is an extremely large number, albeit much less than the number of solutions in F-theory (which at last count is about 10,272,000). And because it’s an extremely large number that betrays something non-trivial and true in particle physics in the real world, it will be studied with the utmost rigor and seriousness, Halverson says.
Further exploration will include identifying stronger links to particle physics in the real world. Researchers must identify the connections or interactions between particles in F-theory solutions, which again depend on the geometric details of extra dimension compactification.
It is quite possible that in the space of a quadrillion solutions there will be some solutions leading to the decay of a proton in foreseeable time scales. This would clearly contradict the real world, since the experiments did not reveal any signs of proton decay. Or physicists could look for solutions that implement the spectrum of particles of the Standard Model, while preserving mathematical symmetry (R-parity). This symmetry forbids certain processes of proton decay and would be very attractive from the point of view of particle physics, but it is absent in modern models.
In addition, this work assumes the existence of supersymmetry - that is, all standard particles have partner particles. String theory needs this symmetry to ensure mathematical consistency of solutions.
But for any theory of supersymmetry to be consistent with the observable universe, symmetry must be broken (just as placing cutlery and a glass on the left or right side out of sync would break the symmetry of the table setting). Otherwise, the partner particles will have the same mass as the particles of the Standard Model - which is definitely not the case, since we have not seen any such partner particles in our experiments.
Ilya Khel