At present, Witten and Pang Xuelin have found the dual relationship between the five perturbation string theories, and if they want to continue to find the remaining dual relationship, it will involve different kinds of cosmic space interpreted by different solutions in the gravitational field equation.

Neither the amount of computation nor the amount of effort required is necessarily any smaller than that of building a theory.

Since Pang Xuelin is not too troublesome and wants to continue his research, Wei Teng will naturally not stop him.

For the next month, Witten continued to write theoretical papers, while Pang Xuelin continued to study the relationship between the analytical solutions of gravitational field equations and quantum field theory in different cases through Ponzi geometry.

This kind of work is very boring, and every day you need to substitute different solutions of gravitational field equations for verification, Schwarzschild gauge, Resler-Norsrum gauge, Kerr solution, Tob-nut solution, Friedman-Lemaître-Robertson-Volcker solution, Gödel universe, Desit universe, anti-Desit space, ......

Verify the past one by one, and the amount of computation is very large.

Time passed day by day, and Pang Xuelin never found a suitable dual relationship.

Just when Pang Xuelin wondered if there was a problem with this calculation method, one night a month later, after Pang Xuelin substituted the analytical solution of the anti-Dessit space into the calculation, the feedback result quickly attracted his attention.

"Hey, I think I've found something amazing......"

Pang Xuelin's eyes lit up.

According to his calculations, there is a dual relationship between the string theory in the 5-dimensional inverse Dessitt space-time (the quantum gravitational theory mentioned above) and the n=4 supersymmetric Yang-Mills theory in the 4-dimensional space-time.

Mathematically, i.e., d=4, n=4, Su(n) Yang-Mills theory and IIB-type string theory are dual in the anti-Desit spacetime of S55.

The specific manifestations are as follows: the symmetry of both theories is PSU(2,2|4), including SO(4,2)O(6), the super-common form is unchanged, and the super-Poincaré is constant.

There is sl(2,)s-duality on both sides, which can be said to be the duality of dualities.

In the big n field theory, n corresponds to an RR manifold of the form 5, i.e., n=∫s5f5.

The coupling constant Gy in the Yang-Mills theory corresponds to the chord coupling constant Gs as follows: Gs = GY2/π, λ = GY2n = L4/α'4.

When λ≈gt; ≈gt; 1, the radius of ads is much larger than the chord length, and the gravitational force can be calculated classically, but the perturbation calculation of field theory fails. When λ≈lt; ≈lt; 1, field theory can perturbate calculations, but string theory is very difficult to calculate.

……

It took a whole night for Pang Xuelin to not only calculate the five-dimensional anti-Desit space-time ads5, but also successively verified the three-dimensional anti-Desit space-time ads3, the four-dimensional anti-Desit space-time, and the seven-dimensional anti-Desit space-time, and finally put forward the following conjectures:

There is a dual relationship between the theory of quantum gravity in the (d+1) dimensional anti-Dessit spacetime and the conformal field theory in the d-dimensional spacetime (this low-dimensional spacetime is the boundary of the (d+1)-dimensional ADS space-time).

To put it more concretely, if there are two worlds, one with five dimensions of space-time and gravitational attraction between objects, and the other world with only four-dimensional space-time and no gravitational force between objects, in general, everyone will think that these two worlds are absolutely completely different. But Pang Xuelin has now found that under one particular circumstance, there is all kinds of evidence that the two worlds can be exactly the same.

Pang Xuelin does not know whether his conjecture is correct, but there is no doubt that if this conjecture is true, then it will represent the importance of human understanding of string theory and quantum gravity theory.

Since it provides a complete definition of the theory of the special cases of anti-Desitian space-time geometry in which negative energy causes space-time to bend in a different way than the universe, physicists can describe the process by which all energy occurs, theoretically even the formation and evaporation of black holes.

What Pang Xuelin didn't know was that the conjecture he put forward was the famous ADS/FT duality in later generations.

This theory was proposed by the Argentine theoretical physicist Juan Maldasina.

It was his discovery that led most theoretical physicists to list theory as a priority candidate for the theory of everything.

In later generations, Mardasina and Witten are listed as the founders of the theory.

Mardasina's paper on ADS/FT duality has become a classic of theoretical physics in later generations, with 16,000 citations, the most cited article in all theoretical physics.

ADS/FT directly feeds more than half of the people in high-energy theory except for PHENO, plus some researchers in condensed matter and quantum information.

In the field of high-energy physics, there has always been the term ADS/FT.

……

Pang Xuelin got up from the chair and stretched out.

Although he hadn't slept all night, his brain was still in a state of high excitement.

Unlike Witten's theoretical research, he is mainly responsible for establishing the mathematical structure of the theory, and Witten is responsible for proposing some ideas in physics.

However, the ADS/FT duality was the first major physics problem he really solved independently, and although he did not know the status of this theory in the physical community in the real world, he knew very well that he had put forward this conjecture, and the physical significance was not much less than that of the theory.

It can be regarded as an important supplement to the theory, and to some extent, the establishment of the mathematical structure of the theory, coupled with the proposal of the ADS/FT duality, Pang Xuelin's contribution to the theory has surpassed that of Edward Witten.

Next, Pang Xuelin spent another whole week writing a paper on the ADS/FT duality.

A week later, Pang Xuelin put his thesis on Edward Witten's desk.

"The Great N Limit of Superconformal Field Theory and Supergravity?"

Edward Witten glanced at Pang Xuelin with some surprise, and then lowered his head and continued to look down.

The office was quiet, the paper written by Pang Xuelin was not long, less than ten pages, but Edward Witten read it for a full two hours.

After a long time, Edward Witten slowly raised his head, looked at Pang Xuelin with a complicated expression, and said with a wry smile: "Pang, I regret it a little, I should have listened to you at that time and continued to cooperate with you in research, I didn't expect you to come up with such an achievement." ”

Pang Xuelin said with a smile: "It's not too late now, why don't you co-sign this paper?" ”

Edward Witten is a big man in the field of theoretical physics, and the two are cooperating in theory, if Witten really wants to co-sign, Pang Xuelin is not easy to refuse.

Edward Witten shook his head and smiled: "Forget it, this is the result of your independent research, I don't want to become a scholar." However, your paper came out just in time, and I have already written the theoretical paper, and the two of us are co-authors, and it happens that these two papers are sent together, and I am ready to submit the paper directly to Science, what do you think? ”

Pang Xuelin said: "I'll leave this to you to deal with, I don't have any opinion." ”

"Okay, that's it!"