Chapter 170: The Beginning of the String Revolution

"I do have some ideas!" Professor Witten nodded and said, "In the process of calculation, after a series of new transformations and values of the equation you gave, I also arrived at a new model, which is different from your model, my model is if the strings are open......

At this time, the eyes of everyone in the office were focused on Professor Witten, and Junxin quickly analyzed the meaning of more than a dozen equations proposed by Professor Witten, and then compared them one by one and found that this should be a variant of superstring theory, but Junxin quickly understood the flaws of this theory.

"Professor Witten, your theory is indeed an explanatory method, and through the transformation of the equation, you are actually transforming the two modes of open and closed strings in the original theory into closed strings. I found in the twelfth equation that you talked about that if you want to make such an assumption, you have to do it under the gauge field of the Yang-Mills equation......"

“…… After this transformation is completed, we return to the original assumptions, and the result is obvious, which is not self-consistent with the Yang-Mills equation, which obviously violates the original self-consistency requirement of superstring theory. ”

Witten frowned and thought about the meaning of the equations that Junxin modified on the blackboard, and at the same time carefully calculated these equations in his heart, and then compared them with his own results, and finally had to admit that what Junxin said was indeed right.

Professor Schwartz said, "What do you think if the twelfth equation is not changed, but the original transformation is removed, and the assumption of the original model is changed to a closed chord?" ”

"You mean, detached from Jun's theoretical model and instead taking the closed chord as the object of study?" Candela asked.

"It shouldn't be that simple!" Strominger also said, his voice a little hoarse, "The professor meant that the closed string and the open string originally had the same meaning, but the two ends of the open string were electrically charged, and if the closed string was the object of study, it would be much simpler." ”

"What do you think, Jun?" Horowitz's words are simple.

Junxin touched his chin and calculated silently in his heart, then picked up the chalk again and wrote a series of formulas on the blackboard and said: "According to Professor Schwartz, then the twelfth equation really does not need to be changed, because it is a formula that considers the effect of open and closed string transformations, but in this way, the situation is a bit complicated. ”

"In my model, the process of conclusion and derivation is actually put into the SO(32) group, and the transformation process can be completely simplified to the calculation of the group. However, your change means that the method of group theory is no longer sufficient to explain it, and a new mathematical structure language is needed to describe it. ”

At this time, Professor Dyson, who was speechless, suddenly said: "What if we don't use mathematical language to describe it, but directly substitute it into the Yang-Mills equation for calculation?" ”

"Then the key is to see whether the final architecture is self-consistent with the original conclusion, if it can be self-consistent, then this is also a solution, a new model. Professor Witten, what do you think? ”

"Jun, I think you can give it a try!"

"Fortunately, although there is no general solution to the Yang-Mills equation, it should still be able to be used for calculation." Junxin said and began to wipe the blackboard again, and started a new round of writing.

"Professor Candela, you have studied a lot of Yang-Mills gauge fields, what do you think of this result?" Strominger asked.

Candela shook his head and said excitedly: "For this, to be honest, I don't know, although this is the direction of my research, but it is not the scope of my research, I have never thought of changing the zero dimension of a point into the one dimension of the string as a fundamental physical unit to construct the Yang-Mills equation, at present, looking at Jun's calculations, I can't see anything for the time being." ”

"If it is supersymmetric, then it means that in addition to the boson, we must also consider the mass fermion, which quantum chromodynamics has been successfully explained, so how can his model be solved?" Candela seemed to be talking to herself, as if she were whispering an inquiry.

"If my calculations are not wrong, then the theory is self-consistent, but this is only a theoretical thing, and if you want to really solve this model, you have to turn it into a mathematical language." After more than half an hour of calculation, Junxin's forehead was also a little more sweaty, and he said with a slightly tired expression.

"Any suggestions?" Horowitz asked.

Witten touched his chin and thought carefully before saying, "I feel that this equation is a little familiar, and it seems that I have heard Professor Thurston mention it." ”

"Professor Thurston is studying topology, so this must be an equation in topology, but what could it be?" Professor Dyson also frowned.

"I guess we can geometry this equation and see how about it?" Strominger suggested.

"I think Professor Strominger's proposal could be considered, but who will do the project? After all, none of us are topologists. Professor Candela agreed.

Professor Witten turned his gaze to Junxin, who knew that Junxin also had a deep knowledge of topology, after all, he had also attended the lecture meeting a few days ago.

"I see, Professor!" Junxin reluctantly picked up the chalk and recalculated, in fact, he already knew the origin of this model after the calculation was completed, it should be the hybrid model of E8*E8, but he couldn't say it immediately, it always had to be calculated to explain everything.

An hour passed quickly, with concentration. Soon, Junxin has completed the geometric calculation of the conclusion.

"What do you think this is?" Professor Witten looked at Junxin and asked.

"It's an interesting manifold and it's interesting." Junxin said with a smile.

"Oh? How so? ”

This is a manifold or complex manifold with a group structure proposed by the famous Norwegian mathematician Sophis-Lee in 1887, and the addition operation and inverse element operation in the group are analytic mappings in the manifold. After this structure was proposed by Sophie-Lee, it was called E8, and this structural model is the hybrid structure of E8*E8. ”

"The one with 248 dimensional symmetry?" Witten suddenly felt a little weak and asked.

"Well, that's it!"

"Well, the math part of the paper on this model is up to you, I don't think I'm up to the task!"

Jun Xin suddenly felt tears streaming down his face: Professor, are you really okay like this? But in the end, Junxin could only nod and agree.

Except for Junxin, no one knew that this paper and Junxin's soon-to-be-completed paper were published in the same issue of Physical Review Letters, which triggered the first revolution in superstring theory. Historians, on the other hand, agree that the five-member panel on superstring theory in Princeton, together with the afternoon discussion between Schwartz and Professor Dyson on soy sauce, was the beginning of the first revolution in superstring theory.