Hide and hide and seeking in 11-dimensional space

The Dirac prize for 2016 was awarded to Arkady Weinstein, Mikhail Shifman from the Fayn Theoretical Physics Institute at the University of Minnesota and Nathan Seiberg from the Institute of Advanced Research of Princeton University. The high award marks outstanding results in quantum chromodynamics outside the framework of the theory of disturbances and the exact results in super-symmetric theories (“To a Better Understanding of Field Theories in the Non-proturbating Regime and in Particular for remuts in Supersymmetric Field Theories " ). The prize is certainly deserved.

What is behind these dry formulations? The main character in this play is a vacuum of quantum chromodynamics (hereinafter KHD)-the theory of strong interactions formulated in the modern form in 1973 by Marri Gell-Mann, Henry Leiteler and Harald Frych. More than 40 years have passed, and how the KHD vacuum is arranged - the main state of the system is so certain and unknown.

A standard spell is pronounced: “KHD vacuum is a dual superconductor”, but the fact that understanding is very approximate, and still not obtained from the first principles of the quantum theory of the field is clear to everyone. The question about the KHD vacuum, or, in other words, the problem of the confinement (retention of the quarks) is rightfully included in the top three of the most important problems of fundamental physics, along with the question of quantum gravity and the nature of dark energy and dark matter.

So, the vacuum of the KHD. We know for sure that the KHD is asymptotically free theory; That is, the elementary particles of the KHD - glows and quarks weakly interact with each other at small distances and strongly interact on large ones. The words “large” and “small” reader must accept with caution: both are one and another refers to very small distances from a macroscopic point of view, and the theory itself sets the scale, regarding which we count the values.

Due to the fact that the force of interaction increases with the distance, a string stretches between the quarks, which does not allow quarks to exist independently-this is the appearance of the confinement (from the English. Confnement-retention, restriction.- Ed. ). How does the KHD string arise and what property of the KHD vacuum responsibly for its occurrence is an extremely complex issue. I note that it was the attempts of a satisfactory description of the scattering of particles in the theory of strong interactions that led to the creation of strings theory in the late 1960s-early 1970s.

Physicists are interested in various properties of particles - mesons and baryons, their decay and transformations. Is it possible to calculate them in a self-compounded way? If you set such a task, then you need to take into account that, like any quantum object, the KHD vacuum is a strongly fluctuating environment, virtual excitation is born and die in it constantly. Moreover, the situation with the KHD vacuum is complicated by the fact that there are two types of vacuum fluctuations that we will call small and large for simplicity.

For clarity, you should imagine a pendulum on a suspension. For him, small fluctuations are small fluctuations in the pendulum regarding the position of equilibrium, and large ones - when the pendulum makes a complete revolution around the suspension point.

Of course, the second process is classically impossible, unless the pendulum is very strong, but we are already in the quantum world in which everything is possible, only with different probability. About large fluctuations we can say that they arise as a result of quantum tunneling and have non -trivial topological properties. In physics, they are called instances , but we will try not to use this term without the need. Their other name is non -transitural fluctuations . For the first time in the quantum theory of fields, they were found in 1975 in the famous work of A. Belavin, A. Polyakov, A. Tupkin and A. Schwartz.

An attentive reader probably already realized that taking into account all fluctuations, large and small, which are also extremely difficult to interact with each other, looks like a hopeless task. But here the union of deep physical intuition and strict mathematical arguments come to the rescue.

The importance of such a union is perfectly understood by all three laureates of the award. In the late 1970s, in a series of works by Arkady Weinstein, Valentina Zakharov and Mikhail Shifman, the rules for the sum of the VIS were formulated, which turned out to be extremely effective for calculating the physical characteristics of strong-composing particles.

How did you manage to resolve the issue of summarizing on all types of vacuum fluctuations, large and small? With the help of elegant mathematical arguments, it was possible to formulate two different performances for different values, without calculating the endless ranks according to fluctuations with unknown coefficients. Comparing the two ideas, it was possible to calculate the characteristics of the particles and formulate the rules of the sums.

But how was it possible to take into account the exclusively complex structure of the KHD vacuum? The complexity of the main state was proposed to be encrypted by a set of so -called vacuum condensates, whose values ​​are world constant. But the condensers are also infinitely many, so at first glance we simply rewrote one unsolvable task through another.

However, it turned out that it is possible to formulate the rules of the amounts so that only two vacuum condensates - curant and glion - will play a key role. These condensates say that in the KHD vacuum, the left-right symmetry and symmetry are disturbed regarding the change in scale. And if the caraudal condensate was known earlier, then the gloss condensate was introduced and found from a comparison with the experiment in these works.

The details of how it arises from the summation according to the large fluctuations of the KHD vacuum are still unknown, but its value with fairly good accuracy is determined. Glyunone condensate gives a contribution to dark energy, and its contribution much exceeds the value known from cosmological data. How this contribution is reduced is an open question.

One of the main hobbies of theorists is the search for new symmetries, and after the symmetry is discovered, the mechanism of its violation is immediately sought as enthusiastically. This happened with the super -symmetry, proposed in 1971 in Fian Yuri Golfand and Evgeny Lichtman. Within the framework of the super -symmetry, the “collectivists” of the bosons and “individualists” of the FERMIONs are united. The synthesis of super -symmetry and KHD led to the creation of super -symmetric quantum chromodynamics - our next character.

The skeptic, of course, will say that super -symmetry in nature has not been found and is just a theoretical toy. We will not argue and so far we will perceive the super -symmetric KHD as an interesting model. Let us ask the same question: how is the vacuum of super -symmetric KHD arranges and how are small and large fluctuations arranged against its background? Firstly, you can strictly show that there is not one vacuum-there are several of them. Secondly, due to additional symmetry, some contractions of undesirable effects occur and there is a hope that a slightly more can be said about a vacuum in such an environment than in a theory without super-symmetry.

In 1982-1984, stanns in a super -symmetric KHD were also studied in a series of works performed at the ITEF - large fluctuations in vacuum. Two new beautiful and unexpected phenomena were discovered that had a great influence on the further development of the quantum theory of fields.

Firstly, it turned out that small fluctuations against the background of a large one (a small trembling of the pendulum with full turn around around the suspension point) know about how the constant of interaction between theory at different scale behaves-the so-called VNSSH (Vainstin-Zakharov-Novikov-Shifman) accurate beta-function was found. This was, apparently, the first example, when in the quantum theory of fields without additional laws of conservation it was possible to accurately take into account the contribution of all small fluctuations in some physically important value.

Secondly, it turned out that there is an unusual situation when two trial objects inserted into different points of space do not know about the distance between these points. This made it possible to calculate one of the vacuum condensates in theory.

Both results were deep, and their importance was not immediately evaluated. The first - about the hidden structure in the interconnection of small and large fluctuations (revitative and non -surpetive) - only now begins to acquire a relatively slender look; The second turned out to be the first example of “topological correlators” in the non -polar theory of fields.

Topological quantum theories of the fields in which the concept of distance was missing were strictly formulated only in the late 1980s in the works of Albert Schwarz and Edward Witten and had a very serious impact on mathematics and its close connection with the quantum theory of the field.

What is the third laureate famous? In 1993-1994, the works of Nathan Zayberg appeared, where what was now called the duality of Zayberg was formulated. The hypothesis was expressed that there are extremely non -trivial connections between different super -symmetric field theories.

It is quite difficult to explain the essence of this hypothesis, so we limit ourselves to the fact that we will try to explain why it is so important. As we have already said many times, there are small and large fluctuations of vacuum. The regime when small fluctuations dominate is called a weak communication regime ; When large - a strong connection regime . It is clear that in a weak communication regime, when the effects of interaction are small, calculations are easier to carry out.

So, the duality of Zayberg binds two theories, one of which is in strong connection, and the second in a weak communication regime. This allows you to get interesting results in the theory with strong connection in this way: we use the transformation of duality and convert it into a weak communication regime in another theory, we carry out relatively simple calculations and broadcast the results of these calculations back into the initial theory. Probably, the actor, who played the role in the new role for himself, finds out something new about himself.

Such a trick allows you to make interesting predictions. For example, elementary particles in one theory may be composite in another. There is still no mathematically strict evidence of Zayberg duality, but it has been very useful for clarifying the physical picture. These works aroused a wave of interest in the concept of duality in a fairly wide context, and now the number of theories related to each other in this or that duality is great.

Moreover, it turned out that different versions of strings theory are interconnected by the transformations of duality, which made it possible to combine all versions of the theory of superstrons into one m-theoria-the theory of the membrane in 11-dimensional space.

Is it possible to accurately take into account all the big vacuum fluctuations? In 1994, two works of Zayberg and Witten appeared, in which in an extended super -symmetric quantum chromodynamics (do not ask what it is) an accurate answer was found for a number of physically important values, including a spectrum of mass of stable particles. Due to the fact that in theory with a super -symmetry, small vacuum fluctuations are relatively easy to take into account, the main problem was reduced to taking into account large fluctuations.

These works still make a strong impression, the authors managed to go along the very edge between exceptional physical intuition and when the not very motivated flight of fantasy begins. On this face, they were kept by the rather thin mathematical results and arguments used.

As a result, with the help of magic spells, which mentioned duality, holomorphic and renormalization group, “they took out a rabbit from the hat” and, not conducting obvious calculations of the contributions of large fluctuations, “guessed” the exact answer, withstanding all simple checks.

At this moment, it seemed that the problem of the confinement in the KHD was about to be resolved. However, joy was premature. In order to explain the confinement in the usual KHD, it was first necessary to break the theory with dilated super -symmetry to the theory with simple super symmetry, and in the second step to break the theory with simple super -symmetry to the KHD, where there is no super -symmetry at all.

The first step was quickly taken, and it was shown that the condensate of monopolists arises - the confinement mechanism expected in the KHD arises due to the summation of large fluctuations. But taking the second step was very difficult, research in this direction continues to the present.

It took almost ten years to get the “guessed” result of Zayberg - Witten from the first principles by direct summation of all large vacuum fluctuations. This was done only in 2002 by Nikita Nekrasov using a beautiful trick.

It turned out that it is convenient to tighten our entire four -dimensional world (three coordinates + time) with a slight angular velocity. Let us allow ourselves a somewhat risky analogy. In the centrifuge we can try to separate those “deposits” that interest us - something similar was made by Nekrasov, and the result of the complete summation of large vacuum fluctuations “in the centrifuge” is now called the statistical amount of Nekrasov. The result of Zayberg - Witten was fully confirmed.

The duality of Zayberg and the decision of Zayberg-Witten were closely related to the geometry of the 11-dimensional space and the picture of the "world on Bran". The reader should gradually get used to the idea that he lives on a six-dimensional surface ("Bran"), embedded in 11-dimensional space. This should please him, or he must come to terms with this, it all depends on temperament.

The duality of Zayberg was simply the Movement of the Bran in the multidimensional space, and the result of the exact summation of large fluctuations around the vacuum state was equivalent to the fact that the form of “our brothers” was accepted by a very specific species. It is the form of Brana that determines the set of stable particles and their masses.

Of course, science is a game with God's hide and seek, where you always play the role of a driver. But the choice of what object we will look for, in our hands, and we must pay tribute to the laureates, they chose extremely worthy of the search for the goal. Of course, it is easier for me to write about Arkady and Misha, until 1990 they worked in Russia and were one of the main actors in the golden decades of the ITEF, in the 1970s and 1980s, when he was certainly in the five leading world centers in theoretical physics. They played an important role in creating a completely unique scientific atmosphere of those years.

When Arkady came to the ITEF from Novosibirsk, and this happened very often, the work began in the morning, and in the evening, when everyone diverged home, loud voices were still heard from the second floor of the theotherapist, and just a scream that a stranger could take to clarify the relationship.

And there only Arkady and Misha, along with co -authors, found out their relations with nature. For 40 years, nothing but hair color has changed. And now everything is the same at the Institute of Theoretical Physics in Minneapolis. Freshmen can envy their enthusiasm for science. The same words relate to Nathan Zayberg.

It is impossible not to mention the exceptional role that he played, and Arkady continues to play in the “upbringing” of younger theorists. He has few formal students, but very many, including the author of these lines, perfectly understand how much he gave them. “Weinstein radius”, a value known in the theory of gravity, frankly, is quite large.

As one colleague said, conferences are divided into boring, to passing quite lively and those in which Weinstein takes part. And Misha Shifman in recent years conveys her enthusiasm for science in books and essays, where the stories of scientists and scientific ideas are read as exciting detectives. Their role in the transfer of the “torch of scientific knowledge” is great, and partly due to the departure of such people, the problem with the institutions of scientific reputation and examination in Russia is so serious.

On this we will finish a short walk along the fluctuating vacuum. As already mentioned, the problem of the confinement in the KHD has stood up and is waiting for its decision. Moreover, it turned out that it is closely related to the problem of building quantum gravity, but this is another story.

The results of the laureates are extremely important and, undoubtedly, will be one of the key elements when finding an answer. There can be only three laureates of the Dirac Prize, this is a restriction in the award of the prize, so I have no doubt that the committee had difficulties with choosing a slightly wider list. The scientific contribution of Valentina Zakharov, Nikita Nekrasov and Viktor Novikov should be noted absolutely. Once again, I congratulate three laureates on this well -deserved reward.