What are Superstrings?

There were two major revolutions in physics in the 20th century: one was the special theory of relativity and the general theory of relativity, which was almost completed by Einstein alone.

Superstring

Right!

Superstring theory is a self-consistent theory established by people abandoning the assumption that elementary particles are point particles and replacing them with the assumption that elementary particles are one-dimensional strings. Various particles in nature are different vibrations of one-dimensional strings. mode. Different from previous quantum field theory and gauge theory, superstring theory requires the existence of gravity, and also requires gauge principle and supersymmetry. There is no doubt that the natural unification of gravity and other interaction forces caused by gauge fields is one of the most attractive features of superstring theory. Therefore, starting from the end of 1984, when people realized that the theory of superstrings can give a unified theory of inclusive standard models, a large number of talented young people naturally devoted themselves to the research of superstring theory.

There were two major revolutions in physics in the 20th century: one was the special theory of relativity and the general theory of relativity, which was almost completed by Einstein alone.

After people's research, we found that

This image can be represented by the figure above. There is only one theory, let's call it the M theory. M theory has a large modal space (the space of various possible vacuums). The five known superstring theories and eleven-dimensional hypergravity are some of the limit regions of M theory or the boundary points of the module space (the sharp points in the figure). The research on the duality of superstrings tells us that no region in the module space is more important and basic than other regions. Each region is only a good description of some properties of M theory. However, we also learned many wonderful properties of duality and M theory in the process of coherently blending these different descriptions, especially the properties of various D-membrane conversions.

Here we have to mention that the superstring theory successfully explained the entropy and radiation of black holes. This is the first time from the microscopic theory to use the basic principles of statistical physics and quantum mechanics to strictly derive the entropy and The radiation formula, without a doubt, establishes that the superstring theory is a correct theory about gravity and other interaction forces.

Unifying 5 superstring theories and 11-dimensional supergravity into M theory is undoubtedly successful, but it also poses greater challenges to people. When the theory of M was proposed, it did not have a strict mathematical expression. Therefore, looking for the mathematical expression of the theory of M and studying the nature of the theory of M carefully became the focus of theoretical physics research in this period.

Douglas (MR) and others have carefully studied the properties of D-membrane and found that at extremely short distances, the interaction between D-membrane can be completely described by gauge theory, and these interactions also include gravitational interactions. Therefore, gravitational interactions at very short distances are actually the quantum effects of gauge theory. Based on these results, Banks (T) and others proposed a basic formulation of the M theory using a zero-dimensional D-film (also referred to as a point D-film) as the basic degree of freedom-matrix theory.

Matrix theory is a non-perturbative Lagrangian representation of the M theory. This representation requires the selection of at least six asymptotically flat directions in the light cone coordinate system and the vacuum background. Using this formulation, many odd conjectures have been proved, and a new class of Lorentz-invariant theories without gravitational interaction has been obtained. If we pay attention to the state with energy of the order of 1 / N (N is the number of rows or columns of the matrix), under the limit of N going to infinity, we can derive a general gauge field theory. There are many indications that under the large N limit, the theory will become simpler, and many degrees of freedom under finite N will not be coupled with physical degrees of freedom and can be completely ignored. All these conclusions are obtained in the light cone coordinate system and finite N. It can be expected that an apparent Lorentz invariant expression will be a very powerful tool for studying the above problems.

Specifically, it is expected that progress will be made on the following issues:

(1) The statistical gauge symmetry of isotactic particles should be derived from a larger continuous gauge symmetry.

(2) The existence of space-time should be related to the cancellation of the contributions of bosons and fermions in the theory of supersymmetry.

(3) As we compact more dimensions, more degrees of freedom will appear in the theory. How can we understand this strange property from the perspective of quantum field theory?

(4) The short-range (ultraviolet) divergence of the effective gravity theory is actually the infrared divergence of some omitted degrees of freedom. These degrees of freedom correspond to the one-dimensional D-film extending between two particles. From the perspective of field theory, See, the nature of these degrees of freedom is very strange.

(5) Link M theory with cosmology.

Obviously, there is not much reason to think that matrix theory is a perfect expression of M theory. It is worth noting that matrix theory does give many meaningful results, so it must also have a physically reasonable component, much like the period before the establishment of quantum mechanics at the beginning of this century (at that time, Planck proposed the energy quantum Derived from the black body radiation formula, Bohr proposed orbital quantization to give a spectrum of hydrogen atoms), some signs and physical connotations of a new theory have been discovered. However, we are far from establishing a perfect self-consistent M theory, so it is necessary to start from the superstring theory to explore its connotation more and deeper.

At the end of 1997, Maldacena's research on the myopic geometry based on D-film found that the type IIB superstring theory compacted on AdS5 × S5 and the large N SU (N) supersymmetry gauge theory are dual, which is expected Solve some basic problems in strongly coupled gauge field theory such as quark confinement and chiral symmetry breaking. As early as the 1970s, & acute; t Hooft proposed: In the case of large N, the planar Feynman diagram in gauge field theory will give the main contribution. From this conclusion, Polykov ( (Polyakov) has long speculated that the large N gauge field theory can be described by (noncritical) string theory, and now Marsena's discovery has made the theory and gauge theory more concrete. Veneziano proposed the string theory in 1968 in order to solve the interaction, and found that the string theory is a unified theory that can be used to unify the four interaction forces. The study of duality led to the M theory. Now Marda Senna's research links M theory and superstring theory with canonical theory (which can be used to describe strong interactions). In a sense, we return to the point of strong interactions. Obviously, we The understanding of the role has been greatly improved, but we have not completely solved the problem of strong interactions, nor have we solved the unified problem of the four interaction forces. Therefore, the study of M theory, superstring theory, and gauge theory is still a Long and very difficult question.

Superstring theory believes that within each elementary particle, a thin line is vibrating, just like the vibration of a string, so this thin line is vividly called a "string" by scientists. We know that different strings vibrate differently, so the tones produced by the vibrations are different. Similarly, the strings inside the particles also have different vibration modes, but the vibration of this string does not generate a tone, but generates particles one by one. In other words, each elementary particle is composed of a string.

Superstring theory believes that particles do not exist, only the strings move in space; different particles are just different vibration modes of strings. All interactions that occur in nature, all matter and energy, can be explained by the splitting and combining of strings.

The movement of a string is so complicated that the three-dimensional space can no longer accommodate its movement trajectory. There must be up to ten dimensions of space to satisfy its movement. Just like the movement of a person is too complex to be completed in a two-dimensional plane, it must The same is done in three-dimensional space.

"Super" here means supersymmetry. In order to unify bosons and fermions, scientists predicted such particles. Due to experimental conditions, it is difficult to find such particles that can prove string theory. As one of the most difficult theories, superstring theory has attracted many theoretical researchers to study it.