Just a few years ago, it seemed that string theory was the new theory of everything. But today the string universe raises more questions than answers
String theory is designed to combine all our knowledge of the Universe and explain it. When she appeared, she literally fascinated with her seeming simplicity and brevity, combining what once seemed impossible. However, over time it became clear that this beautiful theory only seems simple and, unfortunately many researchers, generates much more questions than answers. This theory describes one-dimensional, vibrating fibrous objects called "strings" that spread in space-time and interact with each other. Despite the fact that today other theories are popular among physicists, scientists gradually, piece by piece, continue to discover and decipher the fundamental strings of the physical universe using mathematical models. So, according to a new study, mathematicians from the University of Utah have found new evidence of string theory.
By cleverly combining the ideas of quantum mechanics and general relativity (ODO), string theory, according to physicists, should build a future theory of gravity. Today, however, scientists are increasingly critical of string theory and are less likely to pay attention to it because of the sheer number of questions it raises. However, according to a new study published in the journal, string theory still has a right to exist.
Mathematicians from the University of Utah and the University of St. Louis published the results of mathematical calculations about the two branches of string theory. In the course of the work, the researchers studied a special family of compact K3 surfaces - connected complex two-dimensional surfaces. They are important geometric tools for understanding the symmetries of physical theories.
An example of a cross-section of the K3 surface in a 3-dimensional space used by mathematicians to study the strings of dualities between F-theory and heterotic theory in eight dimensions.
Recall that one of the important features of string theory is that it requires additional measurements of space-time for mathematical consistency. However, not every way to process these additional measurements, also called "compactification," gives a model with the right properties to describe nature. For the so-called eight-dimensional compactification of the string theory modelcalled F-theory, additional measurements must be shaped like the K3 surface.
The team found four unique ways to cut the surfaces of K3 in a particularly useful way, using Jacobian elliptical bundles - complexes of several fibers shaped like a loaf or bagel. Researchers have constructed explicit equations for each of these bundles and have shown that the concepts of string theory in the real physical world have a right to exist.
Example of the K3 surface
"You can think of this family of surfaces as a loaf of bread, and each fiber as a "slice" of this loaf," the researchers write. By studying the sequence of "slices," we can visualize and better understand the whole loaf. According to the authors of the article, an important part of this study is the identification of certain geometric building blocks, called "dividers", inside each K3 surface.
Hours of painstaking work, as a result, allowed mathematicians to prove the theorems of each of the four bundles, and then push each theorem through complex algebraic formulas. The publication quotes the authors of the study as saying that for the last part of this process, scientists used Maple software and a specialized package of differential geometry, which optimized computational efforts.
Our universe is very strange and possibly made up of strings
Since the 1980s, string theory has spawned five versions of its own. And although each of them is built on strings and additional dimensions (all five versions are combined into a general theory of superstrings, my colleague Ilya Hel), in the details of these versions are quite very divergent.
The paradox is that all five versions today can be called equally correct. However, no one was able to prove the presence of strings experimentally. And yet, despite all the skepticism and criticism of string theory, the new work proves its right to exist. Suchthus, string theory cannot be excluded from the list of potential candidates of the Theory of Everything, a universal theory that combines all our knowledge of the world and the universe.
