Superstring theory is a self-consistent theory that people abandon the assumption that the basic particle is a point particle and replace it with the assumption that the basic particle is a one-dimensional chord. All kinds of particles in nature are different vibration modes of one-dimensional strings. Different from the previous quantum field theory and gauge theory, superstring theory needs the existence of gravity, gauge principle and supersymmetry. Undoubtedly, it is one of the most attractive features of superstring theory to naturally unify gravity and other interaction forces caused by gauge fields. Therefore, from the end of 1984, when people realized that superstring theory could give a unified theory including the standard model, a large number of talented young people naturally devoted themselves to the research of superstring theory.
After people's research, it is found that there are actually five self-consistent superstring theories in ten dimensional space. They are two IIAs and IIBs, one is the mixed string theory with the specification of Apin(32)/Z2, the other is the mixed string theory with the specification group of E8×E8, and the other is the I string theory with the specification of SO(32). For a unified theory, five possibilities are still a little too many. So in the past, there were some attempts to deduce these superstring theories from more general theories, but it was not until 1995 that people got a relatively perfect unified picture of these five superstring theories.
This image can be represented by the above picture. There is a unique theory, let's call it M theory. M theory has a large module space (a space composed of various possible vacuums). Five known superstring theories and eleven-dimensional supergravity are some limit regions of M theory or boundary points of module space (sharp points in the figure). The study of superstring duality tells us that no region in module space is more important and basic than other regions, and each region can only describe some properties of M theory. But in the process of combining these different descriptions, I also learned many wonderful properties of duality and M theory, especially the mutual transformation of various D films.
It must be mentioned here that superstring theory has successfully explained the entropy and radiation of black holes. This is the first time to strictly deduce the entropy and radiation formulas of macroscopic black holes from microscopic theory, basic principles of statistical physics and quantum mechanics, and undoubtedly establish that superstring theory is the correct theory about gravity and other interaction forces.
It is undoubtedly successful to unify the five superstring theories and eleven-dimensional supergravity into M theory, but it also poses greater challenges to people. There was no strict mathematical expression when M theory was put forward, so finding the mathematical expression of M theory and studying its properties carefully became the focus of theoretical physics research in this period.
Douglas (MR) and others carefully studied the properties of D films, and found that in a short distance, the interactions between D films can be completely described by gauge theory, and these interactions also include gravitational interactions. So the short-distance gravitational interaction is actually the quantum effect of gauge theory. Based on these results, Banks (T) and others put forward a basic expression of M theory with zero-dimensional D film (also called point D film) as the basic degree of freedom-matrix theory.
Matrix theory is a non-perturbation Lagrangian expression of M theory, which requires that the light cone coordinate system and vacuum background should have at least six asymptotically flat directions. Many even guesses are proved by this expression, and a new Lorentz invariant theory without gravitational interaction is obtained. If we pay attention to the state with energy of 1/N (n is the number of rows or columns of a matrix), a normal gauge field theory can be derived under the limit that n tends to infinity. There are many signs that the theory will become simpler under the big N limit, and many degrees of freedom under the finite N will not be coupled with the degrees of freedom of physics, which can be completely ignored. All these conclusions are obtained in light cone coordinate system and finite N. It can be expected that an obvious expression of Lorentz invariants will be a very powerful tool to study the above problems. Specifically, people expect to make progress in the research on the following issues:
(1) identical particles's statistical gauge symmetry should come from greater continuous gauge symmetry.
(2) The existence of spacetime should be related to the cancellation of boson and fermion contributions in supersymmetry theory.
(3) When we compress more dimensions, theoretically there will be more degrees of freedom. How to understand this strange property from the perspective of quantum field theory?
(4) The short-distance (ultraviolet) divergence of the effective gravity theory is actually some infrared divergence that omits degrees of freedom, corresponding to a one-dimensional D film extending between two particles. From the perspective of field theory, the nature of these degrees of freedom is very strange.
(5) Linking M theory with cosmology.
Obviously, there is not much reason to think that matrix theory is the perfect expression of M theory. It is worth noting that the matrix theory does give many meaningful results, so it must have a physically reasonable composition, which is very similar to the period before the complete establishment of quantum mechanics at the beginning of this century (Planck proposed the energy quantum to derive the blackbody radiation formula, and Bohr proposed the orbital quantization to give the spectrum of hydrogen atoms). Some signs and physical connotations of a brand-new theory have been discovered. However, we are far from establishing a perfect self-consistent M theory, so it is necessary to explore its connotation from superstring theory. In this respect, the research of superstring theory has made a new breakthrough.
At the end of 1997, Maldacena of Marda's research on myopia binding geometry based on D-film found that the IIB-type superstring theory compacted on AdS5×S5 is dual with the large N SU(N) supersymmetric gauge theory, which is expected to solve some basic problems in the strongly coupled gauge field theory, such as quark confinement and chiral symmetry breaking. As early as the 1970s, Hooft (? T Hooft) proposed that the plane Feynman diagram in gauge field theory will make a great contribution when n is large. Starting from this conclusion, poliakov speculated long ago that gauge field theory of big N can be described by (non-critical) string theory, and now massena's discovery makes this theory and gauge theory more specific. 1968, Veneziano put forward the string theory to solve the interaction, and found that string theory is a unified theory, which can be used to unify the four kinds of interaction forces. The study of duality led to M theory. Now Marda Senna's research links M theory and superstring theory with gauge theory (gauge theory can be used to describe strong interaction). In a sense, we are back to the point of strong interaction. Obviously, our understanding of strong interaction has been greatly improved, but we still haven't completely solved the problem of strong interaction, and we haven't solved the unification of the four kinds of interaction forces, so the research on M theory, superstring theory and gauge theory is still a long-term and very difficult problem.
Theoretical model superstring theory holds that there is a thin line vibrating inside each elementary particle, just like the vibration of a string, so this thin line is called "string" by scientists. We know that different strings vibrate in different modes, so the vibration produces different tones. Similarly, the string inside the particle also has different vibration modes, but the vibration of this string does not produce tones, but particles. In other words, each elementary particle is composed of a string.
According to superstring theory, particles do not exist, only strings move in space; Different particles are just different vibration modes of strings. All interactions in nature, all matter and energy can be explained by the splitting and combination of strings.
The motion of a string is so complicated that the three-dimensional space can no longer accommodate its trajectory, and it must have a space as high as ten dimensions to satisfy its motion, just as human motion is so complicated that it cannot be completed in the two-dimensional plane and must be completed in the three-dimensional space.