From failed candidate to chief scientist

Chapter 182 AdSCFT Conjecture
Jiang Fanjun and Zhao Bo acted very quickly. Early the next morning, they had already embarked on their journey. Jiang Fanjun boarded a flight to Chou Country, and Zhao Bo also headed straight for Beiyang.

Shan Gang continued to run around decorating the laboratory and purchasing equipment. She was extremely busy and could not see anyone all day long. She needed to set up the turbulence laboratory as soon as possible and strive to put it into research use as soon as possible.

The originally bustling mathematics research center was empty again.

Lin Mo once again started his life of taking classes, working out, and doing research.

At this time, Lin Mozhen was immersed in dealing with the problem at hand-the AdS/CFT conjecture.

AdS/CFT in the narrow sense means that the gravity theory in a 5-dimensional AdS space becomes a (fixed point) quantum field theory in 4-dimensional space-time at the AdS boundary.

This allows gravity theory and quantum theory to be organically integrated into one.

Therefore, it goes without saying how important it is to prove the significance of this conjecture. It is not an exaggeration to call it a revolution in physical theory. Many existing string theory studies are based on this conjecture.

Proving this will make the research on string theory take an extremely important step.

It sounds very complicated to prove this, but if you turn it into a mathematical problem, it will be easier to understand.

To explain in mathematical language, AdS/CFT is actually the Poisson integral formula in complex variable functions. The holomorphic function on the disk can represent a certain integral of the paired boundary.

That is, body = boundary, this is the mathematical explanation of AdS/CFT, which sounds easy.

But it is not easy to prove it.

Lin Mo initially tried to start with functions and use functional methods to prove the solution to this problem. However, after conducting research for a period of time, Lin Mo found that this path would not work because there were too many variables in simply constructing functions. It is impossible to proceed further.

After a few days of thinking, Lin Mo changed his mind. What he was doing now was to construct a five-dimensional sphere, select a point on its surface, and prove that this point on the five-dimensional sphere is equivalent to a point in the four-dimensional space. ball to prove this conjecture.

This was also not easy, but it was not as clueless as before. Moreover, the feedback given by the system made Lin Mo think that his new idea should be correct.

However, Lin Mo was still scratching his head when it came to multi-dimensional space.

For several days, Lin Mo's research made no substantial progress.

At this moment, Lin Mo suddenly remembered someone, took out his cell phone and sent a message.

The other person responded quickly.

After receiving the reply, Lin Mo made a video call.

"Oh, dear Lin, how are you? I still have some things to deal with here, and it still takes a little time..."

Marina's familiar face appeared on the opposite side of the video.

Yes, the person Lin Mo thought of was Marina Vyazovska.

The reason why I think of Marina is because Marina has done research on the filling problem of spheres in eight-dimensional space and achieved great results. After her research, she gave the maximum filling of spheres in eight-dimensional space. density.

Speaking of this, we have to mention Kepler's conjecture.

Kepler's conjecture: How to fill space with spheres of the same size to maximize the filling density?
So many mathematicians got involved and came up with various ways of filling balls. In order to prove this conjecture, mathematicians spent 400 years.

However, Kepler's conjecture only discusses filling in three-dimensional space, so what about filling in higher dimensions?In the hundreds of years after Kepler's conjecture was proved, mathematicians have devoted themselves to the study of sphere filling problems in high-dimensional space.

And Marina became the first person to solve the problem of filling a sphere in eight-dimensional space.

After that, Marina also extended the eight-dimensional space to 24 dimensions.

Therefore, Marina has conducted in-depth research on dimensional space and has very rich experience.

At this time, Lin Mo encountered obstacles in studying the problem of spheres in four- and five-dimensional spaces, and he thought of Marina.

"Oh, Marina, I didn't disturb your rest." "No, I have nothing to do here for the time being."

"That's good, Marina. First of all, I have no intention of urging you to come back. I just encountered some problems in my research and want to communicate with you."

"Oh?"

Marina on the opposite side was obviously stunned for a moment.

"How can you think that there is still a problem? Lin, this is simply unbelievable. Come on, tell me what the problem is."

Marina immediately became interested.

"That's it..."

Lin Mo introduced the topic he was researching and his research ideas to Marina.

"A point on a sphere in five-dimensional space is equivalent to a sphere in four-dimensional space?"

Marina frowned.

"Lin, don't tell me that you are studying string theory."

Lin Mo shrugged and nodded.

"Oh my God, Lin, how can you do string theory, you know, string theory is..."

"Okay, Marina, I know what you are going to say, but I have already started and I don't plan to give up. Moreover, I feel that I have found the right research direction now, so maybe I can really prove it? "

Before Marina could finish speaking, Lin Mo interrupted Marina's words of admonishment and brought the topic back to research.

"So, Marina, I know that you have done in-depth research on multi-dimensional space. I was wondering if you could share with me your experience in this area."

"so……"

Marina glanced at Lin Mo on the other side of the screen and knew that she could not change Lin Mo's decision, so she had no choice but to bring her thoughts back to the research problem itself.

"Let me think."

Silence fell across the screen.

Lin Mo didn't rush and waited quietly.

I don’t know how long it took, but Marina’s voice came from the other side of the screen again.

"If you want to ask me about the volumes of spheres in different dimensions, I might be able to tell you some information, but..."

Marina frowned slightly, with a hint of annoyance in her tone.

"It's okay, Marina, just tell me what you know. My understanding of multi-dimensional space is still limited, and you can just help me supplement this knowledge."

"OK then."

"Then let's first talk about what high dimensions are, so they are called high latitudes..."

"As for spheres in high-dimensional space, they are like this..."

"As for the volume and density of spheres in high-latitude space, their calculation formulas..."

Marina explained her understanding and research on high-latitude space spheres to Lin Mo without any secrets, and popularized science in simple and in-depth terms.

(End of this chapter)