Physicists who wandered through the "landscape" theorystrings — spaces of billions and billions of mathematical solutions to a theory in which each solution provides equations that physicists try to describe reality — stumbled upon a subset of such equations that include as many particles of matter as exist in our Universe. However, this is a huge subset: there is at least a quadrillion of such solutions. This is the largest find in the history of string theory.

String theory

According to string theory, all particles andfundamental forces arise in the process of vibrations of 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 dimension, the additional six dimensions are “compactified”, so that they cannot be detected.

Different compactifications lead to different solutions. In string theory, "solution" implies a vacuum of space-time, which is governed by Einstein's theory of gravity in combination 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 concentrated theirefforts to try to find ways to connect string theory with the properties of our well-known observable Universe — in particular, the Standard Model of particle physics, which describes all known particles and forces except gravity.

Most of these efforts are related to the versionstring theory in which the strings interact weakly. However, over the past twenty years, a new branch of string theory called F-theory has allowed physicists to work with strongly interacting - or strongly connected - strings.

“The interesting results are that when the connection is large, we can begin to describe the theory very geometrically,” says Mirjam Tsvetik from the University of Pennsylvania in Philadelphia.

This means that string theorists canuse algebraic geometry — which uses algebraic methods for solving geometric problems — to analyze various compactification methods of extra dimensions in F-theory and search for solutions. Mathematicians independently study some geometric shapes that appear in F-theory. “They provide us, physicists, with extensive tools,” says Ling Ling, also from the University of Pennsylvania. "Geometry is actually very important, it is the" language "that makes the F-theory a powerful structure."

Quadrillions of universes

And so, Flower, Lin, James Halverson fromNortheastern 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 particles of matter) as described by the Standard Model - including the feature by which fermions are three generations (for example, an electron , muon and tau are three generations of the same type of fermion).

F-theory solutions discovered by Flower and hercolleagues also include particles that demonstrate chirality (no symmetry with respect to the right and left side) of the Standard Model. In the terminology of particle physics, these solutions reproduce the exact “chiral spectrum” of particles of the Standard Model. For example, quarks and leptons in these solutions have left and right versions, as in our Universe.

New job shows that there isat least a quadrillion solutions in which particles have the same chiral spectrum as in the Standard Model, which is 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,” says Tsvetik. “What is surprising and pleasant is that it’s all in the mode of tightly coupled string theory, where geometry helps us.”

A quadrillion is an extremely large number, althoughand much less than the number of solutions in the F-theory (which, according to recent calculations, is of the order of 10272000). And since this is an extremely large number that gives out something non-trivial and true in the physics of particles of the real world, it will be studied with all rigor and seriousness, says Halverson.

Further study will includeidentifying stronger connections with real-world elementary particle physics. Researchers must determine the connections or interactions between particles in F-theory solutions, which again depend on the geometric details of the compactification of the extra dimensions.

It is possible that in quadrillion spacedecisions will be some decisions leading to proton decay in a foreseeable time scale. This would clearly contradict the real world, since the experiments did not reveal any signs of proton decay. Or, physicists could search for solutions that implement the spectrum of the particles of the Standard Model, preserving mathematical symmetry (R-parity). This symmetry prohibits certain processes of proton decay and would be very attractive from the point of view of particle physics, however, it is absent in modern models.

In addition, this work assumes the existencesupersymmetries - that is, all standard particles have partner particles. String theory needs this symmetry to ensure mathematical consistency of solutions.

But in order for any supersymmetry theorycorresponded to the observable universe, the symmetry must be broken (just as the installation of cutlery and glass on the left or right side at once breaks the symmetry of the table setting). Otherwise, the partner particles will have the same mass as the particles of the Standard Model - and this is definitely not the case, since we have not seen any similar partner particles in our experiments.

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