The most important point of M-theory is that it adds the study of non-perturbated strings to the superstring theory.

In addition to one-dimensional strings, non-perturbative string theory also includes high-dimensional objects such as two-dimensional membranes and tricones (collectively referred to as membranes).

Before Pang Xuelin and Witten officially began to study M theory, the international physics community generally believed that superstring theory and supermembranes with a spatial dimension greater than one were two different theories, and there was no necessary connection between them.

However, as Pang Xuelin and Witten began their research on non-perturbative string theory, they found that on the basis of unifying quantum mechanics and general relativity, they could not only connect one-dimensional strings with other supermembranes, but also unify other supermembranes within the same theoretical framework.

These superfilms are the unified dynamic objects of the theory, especially when the interaction of strings is large (i.e., the chords are in the non-perturbation region), and the dynamic effects of these high-dimensional films are more important than those of one-dimensional strings.

To a certain extent, this proves why the perturbation string cannot give a complete theoretical framework for low-energy physics, because it ignores the more important kinetic effects of high-dimensional membranes.

Therefore, in the past six months, Pang Xuelin and Witten have been establishing the dual relationship between five different superstring theories through Ponzi geometry.

There are two main types of duals, one is S duality and the other is T duality.

The so-called duality, which is essentially a mathematical concept, is defined as follows: if two logical formulas are equal, then their duality is also equal.

Here, it refers to the fact that there is actually some degree of equivalence between two seemingly different physical theories.

S duality refers to a set of strongly interacting particles in perturbation string theory, which in some cases can be regarded as a set of weakly interacting particles in a completely different theory.

T duality means that a string propagating in a ring of radius R is equivalent to a string propagating in a ring with radius of 1/R.

They found that the I-string theory is equivalent to the SO(32) hybrid string theory under the S duality.

Type IIA string theory, which is equivalent to type IIB string theory in T duality.

……

Through the various dualities and equivalence relations between the five string theories and the eleven-dimensional supergravity, the five string theories can be unified.

Each of these five string theories is the result of a different limit case of M-theory.

This was Witten's theory of M in the real world, which led to the second superstring revolution.

M-theory reveals the nature of interactions, as well as space-time, suggesting their non-fundamentality.

In particular, the theory predicts the existence of extra dimensions and supersymmetry, providing a microscopic explanation for some black hole entropy for the first time.

However, in the process of establishing the M theory, Pang Xuelin and Witten also discovered some problems.

The first is the problem of vacuum.

There are various vacuum states in M theory, and given mathematical calculations, they conservatively estimate that there is at least 10^500 such a vacuum solution.

And the physical and cosmological constants of each vacuum solution are different.

Recent cosmological observations have shown that the universe in which the Earth is located has a small positive cosmic constant, which governs the current accelerating expansion of the universe and constitutes the main matter (dark matter and dark energy) in the universe.

How to find the vacuum solution of the existing universe from the many vacuum solutions and give a first-principles explanation is a question that M theory needs to answer.

Second, M-theory needs to answer the question of the source and nature of dark energy.

According to Pang Xuelin's calculations, the cosmological model of the early universe explosion can be given through the M theory, and even the tensor perturbation in the very early stage of the universe can be directly calculated to be much smaller than the scalar perturbation.

This is consistent with the latest cosmological observations.

However, when it comes to dark energy and dark matter, there is no way to give a reasonable explanation for it at present.

Thirdly, they also found that there are also certain difficulties in M-theory in how to explain the strong coupling behavior in quantum chromodynamics, such as the vacuum properties of quantum chromodynamics, the quark-gluon plasma properties under high temperature conditions, and so on.

For the first two questions, neither Pang Xuelin nor Witten have done much research.

They are well aware that under the existing experimental conditions and astronomical observations, there is no way to make further breakthroughs in these two problems for the time being.

But on the third issue, Pang Xuelin and Witten disagreed.

"Pong, our M theory has perfectly unified the five-string theory and the eleven-dimensional supergravity, and although we can't be sure that our theory is completely correct, these seamless dualities and other wonderful relationships between the theory are enough to prove that we have nothing wrong with the general direction......"

On the small terrace of the villa, Witten was drinking tea while smiling at Pang Xuelin.

In the past six months, the research has gone even more smoothly than he imagined.

In particular, the various duality relationships established by Ponzi geometry are used to link the different perturbation string theories very cleverly.

Witten is sure that this achievement, once presented, will definitely cause a sensation in the physics community.

If it were not for the existing experimental conditions that could not verify this theory, the significance of this theory in the history of physics is comparable to Einstein's theory of relativity and quantum mechanics established by Max Planck, Niels Bohr, Werner Heisenberg, Erwin Schrödinger and others.

But just when he thought he could write a paper to show this great achievement to the physics community, Pang Xuelin objected.

"Professor Witten, I don't think we need to be in such a hurry." Pang Xuelin said, "According to my previous calculations, M theory can explain the strong coupling behavior in quantum chromodynamics, but now there is no way to explain it, and we must have missed something." ”

In fact, this is not only the result of calculations, but also in the real world, Pang Xuelin has also learned quantum chromodynamics in the process of learning materials science and chemistry.

He remembers very well that in the real world, the problem of strong coupling in quantum chromodynamics has been solved and has been applied in condensed matter physics, materials science, and other fields.

Witten smiled: "Pang, the results we have achieved so far have been quite perfect, even if there are still some dualities that we have not found out, but it is enough to support the existing theoretical framework system, we don't need to continue to nitpick." ”

Pang Xuelin was slightly stunned, his eyes suddenly lit up, and he said, "Professor Witten, what did you just say?" ”

Witten said: "There's no need to continue to nitpick. ”

"No, it's the last sentence."

"The last sentence? We've done it perfectly, even if we haven't figured out some of the dualities......"

"Yes, it's a dual relationship!"

Pang Xuelin slapped his palms and said, "Professor Witten, in this way, why don't you write the paper first, and I will continue to study on the basis of the present, what do you think?" ”

"Okay!"

Witten hesitated for a moment and nodded.