Lecture
String theory is the direction of theoretical physics that studies the dynamics of the interaction of not one-point particles [1] , but one-dimensional extended objects, so-called quantum strings [2] . String theory combines the ideas of quantum mechanics and the theory of relativity, so the future theory of quantum gravity may be built on its basis [3] [4] .
String theory is based on the hypothesis [5] that all elementary particles and their fundamental interactions arise as a result of vibrations and interactions of ultramicroscopic quantum strings on scales of the order of a Planck length of 10 −35 m [2] . This approach, on the one hand, allows us to avoid such difficulties of quantum field theory as renormalization [6] , and, on the other hand, leads to a deeper look at the structure of matter and space-time [6] . Quantum theory of strings arose in the early 1970s as a result of the conceptualization of Gabriele Veneziano’s formulas [7] related to string models of the structure of hadrons. The mid-1980s and mid-1990s were marked by the rapid development of string theory, and it was expected that the so-called “unified theory” or “theory of everything” [4] would be formulated on the basis of string theory, which Einstein unsuccessfully dedicated to decades [ 8] . But, in spite of the mathematical rigor and integrity of the theory, the variants of experimental confirmation of string theory have not yet been found [2] . The theory that arose for describing hadron physics, but not quite suitable for this, turned out to be in a kind of experimental vacuum describing all interactions.
One of the main problems when attempting to describe the procedure for reducing string theories from dimension 26 or 10 [9] to low-energy physics of dimension 4 is the large number of compactifications of extra dimensions on Calabi-Yau manifolds and on orbifolds, which are probably special limiting cases of spaces Calabi - Yau [10] . A large number of possible solutions since the late 1970s and early 1980s created a problem known as the “landscape problem” [11] , and therefore some scientists doubt whether string theory deserves scientific status [12] .
Despite these difficulties, the development of string theory stimulated the development of mathematical formalisms, mainly algebraic and differential geometry, topology, and also allowed a deeper understanding of the structure of the preceding theories of quantum gravity [2] . The development of string theory continues, and there is hope [2] that the missing elements of string theories and the corresponding phenomena will be found in the near future, including as a result of experiments at the Large Hadron Collider [13] .
If there were an explicit mechanism for extrapolating strings into low-energy physics, string theory would present all fundamental particles and their interactions as constraints on the excitation spectra of non-local one-dimensional objects. The characteristic dimensions of compactified strings are extremely small, of the order of 10–33 cm (of the order of the Planck length) [14] ; therefore, they are inaccessible for observation in experiment [2] . Similar to the vibrations of the strings of musical instruments, the spectral components of the strings are possible only for certain frequencies (quantum amplitudes). The higher the frequency, the greater the energy accumulated in such a vibration [15] , and, in accordance with the formula E = mc², the greater the mass of the particle, in the role of which the oscillating string manifests itself in the observed world. A parameter similar to the frequency for an oscillator, for a string, is the square of the mass [16] .
Consistent and self-consistent quantum string theories are possible only in spaces of higher dimension (more than four, taking into account the dimension associated with time). In this connection, the question of the dimension of space-time is opened in string physics [17] . The fact that in the macroscopic (directly observable) world additional spatial dimensions are not observed is explained in string theories by one of two possible mechanisms: compactification of these dimensions is twisting to dimensions of the order of a Planck length, or localization of all particles of a multidimensional universe (multiverse) on a four-dimensional world sheet which is the observable part of the multiverse. It is assumed that higher dimensions may manifest themselves in interactions of elementary particles at high energies, but so far there are no experimental indications of such manifestations.
When constructing string theory distinguish the approach of primary and secondary quantization. The latter operates with the notion of a string field - a functional on the loop space, like quantum field theory. In the primary quantization formalism, mathematical methods describe the motion of a test string in external string fields, and the interaction between strings, including the decay and union of strings, is not excluded. The primary quantization approach links string theory with ordinary field theory on the world surface [4] .
The most realistic string theories include supersymmetry as a mandatory element; therefore, such theories are called superstrings [18] . The set of particles and interactions between them, observed at relatively low energies, practically reproduces the structure of the standard model in elementary particle physics, and many properties of the standard model receive an elegant explanation in the framework of superstring theories. Nevertheless, there are still no principles with the help of which one or other limitations of string theories could be explained in order to obtain a certain similarity to the standard model [19] .
In the mid-1980s, Michael Green and John Schwartz came to the conclusion that supersymmetry, which is central to string theory, can be included in it not in one but in two ways: the first is supersymmetry of the world surface of the string [4] , the second is spatial -time supersymmetry [20] . Basically, these methods of introducing supersymmetry connect methods of conformal field theory with standard methods of quantum field theory [21] [22] . The technical features of the implementation of these methods of introducing supersymmetry led to the emergence of five different theories of superstrings — type I, types IIA and IIB, and two heterotic string theories [23] . The resulting surge in interest in string theory was called "the first superstring revolution." All these models are formulated in 10-dimensional space-time, but differ in string spectra and gauge symmetry groups. The construction of 11-dimensional supergravity, developed in the 1970s and developed in the 1980s [24] , as well as unusual topological duality of phase variables in string theory in the mid-1990s led to a “second superstring revolution”. It turned out that all these theories, in fact, are closely related to each other thanks to certain dualities [25] . It has been suggested that all five theories are different limiting cases of a unified fundamental theory, called M-theory. Currently, an adequate mathematical language is being sought to formulate this theory [19] .
Strings as fundamental objects were originally introduced into the physics of elementary particles to explain the structural features of hadrons, in particular pions.
In the 1960s, a relationship was found between the hadron spin and its mass (Chu – Frauchi graph) [26] [27] . This observation led to the creation of the Regge theory, in which different hadrons were considered not as elementary particles, but as various manifestations of a single extended object — the Reggeon. In subsequent years, the efforts of Gabriele Veneziano, Yoichiro Nambu, Holger Bech Nielsen, and Leonard Susskind developed a formula for the dispersion of reggeons and gave a string interpretation of the phenomena involved.
In 1968, Gabriele Veneziano and Mahiko Suzuki, when trying to analyze the process of collisions of pi-mesons (pions), found that the amplitude of the pair scattering of high-energy pions was very accurately described by one of the beta functions introduced by Leonard Euler in 1730. It was later established that the pair pion scattering amplitude can be decomposed into an infinite series, the beginning of which coincides with the Veneziano – Suzuki formula [28] .
In 1970, Yoichiro Nambu, Tetsuo Goto, Holger Beh Nielsen and Leonard Susskind came up with the idea that the interaction between the colliding peonies is due to the fact that these peonies are connected by an “infinitely thin oscillating thread”. Believing that this “thread” obeys the laws of quantum mechanics, they derived a formula that coincides with the Veneziano – Suzuki formula. Thus, models have appeared in which elementary particles are represented as one-dimensional strings that vibrate at certain notes (frequencies) [28] .
With the advent of quantum chromodynamics, the scientific community lost interest in string theory in hadron physics until the 1980s. XX century. [2]
By 1974, it became clear that string theories based on Veneziano formulas were implemented in a dimension of space greater than 4: the Veneziano model and the Shapiro-Virasoro model (SV) in dimension 26, and the Ramon-Nevyö model - Schwarz (R-NS) at 10, and they all predict tachyons [29] . The speed of tachyons exceeds the speed of light in a vacuum, and therefore their existence is contrary to the principle of causality, which, in turn, is violated in the microworld. Thus, there is no convincing (first of all, experimental) evidence of the existence of a tachyon, as well as logically invulnerable refutations [30] . At the moment, it is considered preferable not to use the idea of tachyons when constructing physical theories. The solution of the tachyon problem is based on works on the space-time global (coordinate-independent) Wess-Zumino supersymmetry (1974). [31] . In 1977, Gliozzi, Scherk and Olive (GSO projection) introduced a special projection for string variables into the R-NS model, which eliminated the tachyon and essentially gave a supersymmetric string [32] . In 1981, Green and Schwartz managed to describe the GSO projection in terms of D-dimensional supersymmetry and later introduce the principle of eliminating anomalies in string theories [33] .
In 1974, John Schwartz and Joel Sherk, and independently of them Tamiaki Onayya, studying the properties of some string vibrations, found that they exactly correspond to the properties of a hypothetical particle - a quantum of the gravitational field called graviton [34] . Schwartz and Scherk argued that string theory initially failed because physicists underestimated its scale [19] . Based on this model, a boson string theory was created [4] , which still remains the first version of string theory taught to students [35] . This theory is formulated in terms of Polyakov’s action, which can be used to predict the movement of a string in space and time. The quantization procedure for Polyakov’s action leads to the fact that the string can vibrate in various ways and each method of its vibration generates a separate elementary particle. The mass of the particle and the characteristics of its interaction are determined by the method of vibration of the string, or a kind of “note” that is extracted from the string. The resulting gamma is called the mass spectrum of string theory.
The original models included both open strings, that is, threads having two free ends, as well as closed ones, that is, loops. These two types of strings behave differently and generate two different spectra. Not all modern string theories use both types, some cost only closed strings.
The theory of boson strings is not without problems. First of all, the theory has a fundamental instability, which implies the disintegration of space-time itself. In addition, as its name implies, the spectrum of particles is limited only by bosons. Despite the fact that bosons are an important ingredient in the universe, the universe does not consist only of them. She also predicts a non-existent particle with a negative square of mass - tachyon [16] . Research into how fermions can be included in the spectrum of string theory has led to the concept of supersymmetry - the theory of the interrelation of bosons and fermions, which now has an independent meaning. Theories that include fermion vibration of strings are called superstring theories [36] .
In 1984-1986 physicists realized that string theory could describe all the elementary particles and the interactions between them, and hundreds of scientists began working on string theory as the most promising idea of combining physical theories. The beginning of this first superstring revolution was laid by the discovery in 1984 by Michael Green and John Schwartz of the phenomenon of reduction of anomalies in the theory of strings of type I. The mechanism of this reduction is called the Green – Schwartz mechanism. Other significant discoveries, such as the discovery of a heterotic string, were made in 1985 [19] .
In the mid-1990s, Edward Witten, Joseph Polchinski, and other physicists discovered strong evidence that various superstring theories are different limiting cases of an 11-dimensional M-theory that has not yet been developed. This discovery marked the second superstring revolution . Recent studies of string theory (more precisely, M-theory) affect D-branes, multidimensional objects, the existence of which follows from the inclusion in the theory of open strings [19] .
In 1997, Juan Maldacena discovered the relationship between string theory and gauge theory, which is called the N = 4 supersymmetric Yang-Mills theory [4] . This interconnection, which is called the AdS / CFT correspondence (the abbreviation of the terms anti de Sitter space is the anti-de Sitter space, and the conformal field theory is the conformal field theory), attracted much interest from the string community and is being actively studied [37] . AdS / CFT correspondence is a concrete realization of the holographic principle, which has far-reaching consequences with regard to black holes, locality and information in physics, as well as the nature of gravitational interaction.
In 2003, the discovery of the landscape of string theory, meaning the existence of an exponentially large number of nonequivalent spurious vacuums in string theory [38] [39] [40] , gave rise to a discussion about what string theory can predict and how string cosmology can change ( see below for details).
Among the many properties of string theory, three of the following are particularly important:
| Type of | The number of dimensions of space-time | Characteristic |
|---|---|---|
| Bosonic | 26 | Describes only bosons, no fermions; strings both open and closed; main drawback: a particle with an imaginary mass, moving at a speed greater than the speed of light - tachyon |
| I | ten | Includes supersymmetry; strings both open and closed; no tachyon; group symmetry - SO (32) |
| IIA | ten | Includes supersymmetry; strings only closed; no tachyon; massless fermions are not chiral |
| IIB | ten | Includes supersymmetry; strings only closed; no tachyon; massless fermions are chiral |
| HO | ten | Includes supersymmetry; strings only closed; no tachyon; heterotic theory: strings, oscillating clockwise, differ from strings, oscillating against; group symmetry - SO (32) |
| He | ten | Includes supersymmetry; strings only closed; no tachyon; heterotic theory: strings, oscillating clockwise, differ from strings, oscillating against; group symmetry - E 8 × E 8 |
Несмотря на то, что понимание деталей суперструнных теорий требует серьёзной математической подготовки, некоторые качественные свойства квантовых струн можно понять на интуитивном уровне. Так, квантовые струны, как и обычные струны, обладают упругостью, которая считается фундаментальным параметром теории. Упругость квантовой струны тесно связана с её размером. Рассмотрим замкнутую струну, к которой не приложены никакие силы. Упругость струны будет стремиться стянуть её в более мелкую петлю вплоть до размера точки. Однако это нарушило бы один из фундаментальных принципов квантовой механики — принцип неопределённости Гейзенберга. Характерный размер струнной петли получится в результате балансирования между силой упругости, сокращающей струну, и эффектом неопределённости, растягивающим струну.
Благодаря протяжённости струны решается проблема ультрафиолетовых расходимостей в квантовой теории поля, и, следовательно, вся процедура регуляризации иперенормировки перестаёт быть математическим трюком и обретает физический смысл. Действительно, в квантовой теории поля бесконечные значения амплитуд взаимодействия возникают в результате того, что две частицы могут сколь угодно близко подойти друг к другу. В теории струн это уже невозможно: слишком близко расположенные струны сливаются в струну [6] .
В середине 1980-х было установлено, что суперсимметрия, являющаяся центральным звеном теории струн [42] , может быть включена в неё не одним, а пятью различными способами, что приводит к пяти различным теориям: типа I, типов IIA и IIB, и две гетеротические струнные теории. Можно предположить, что только одна из них могла претендовать на роль «теории всего», причём та, которая при низких энергиях и компактифицированных шести дополнительных измерениях согласовывалась бы с реальными наблюдениями. Оставались открытыми вопросы о том, какая именно теория более адекватна и что делать с остальными четырьмя теориями [19] С. 126 .
В ходе второй суперструнной революции было показано, что такое представление неверно: все пять суперструнных теорий тесно связаны друг с другом, являясь различными предельными случаями единой 11-мерной фундаментальной теории (М-теория) [19] [43] .
Все пять суперструнных теорий связаны друг с другом преобразованиями, называемыми дуальностями [44] . Если две теории связаны между собой преобразованием дуальности (дуальным преобразованием), это означает, что каждое явление и качество из одной теории в каком-нибудь предельном случае имеет свой аналог в другой теории, а также имеется некий своеобразный «словарь» перевода из одной теории в другую [45] .
То есть дуальности связывают и величины, которые считались различными или даже взаимоисключающими. Большие и малые масштабы, сильные и слабые константы связи — эти величины всегда считались совершенно чёткими пределами поведения физических систем как в классической теории поля, так и в квантовой. Струны, тем не менее, могут устранять различия между большим и малым, сильным и слабым.
Т-дуальность связана с симметрией в теории струн, применимой к струнным теориям типа IIA и IIB и двум гетеротическим струнным теориям. Преобразования Т-дуальности действуют в пространствах, в которых по крайней мере одна область имеет топологию окружности. При таком преобразовании радиус R этой области меняется на 1/ R , и «намотанные» [46] состояния струн меняются на высокоимпульсные струнные состояния в дуальной теории. Таким образом, меняя импульсные моды и винтовые моды струны, можно переключаться между крупным и мелким масштабом [47] .
Другими словами связь теории типа IIA с теорией типа IIB означает, что их можно компактифицировать на окружность, а затем, поменяв винтовые и импульсные моды, а значит, и масштабы, можно увидеть, что теории поменялись местами. То же самое верно и для двух гетеротических теорий [48] .
S-дуальность (сильно-слабая дуальность) − эквивалентность двух квантовых теорий поля, теории струн и M-теории. Преобразование S-дуальности заменяет физические состояния и вакуум с константой связи [49] g одной теории на физические состояния и вакуум с константой связи 1 / g другой, дуальной первой теории. Благодаря этому оказывается возможным использовать теорию возмущений, которая справедлива для теорий с константой связи g много меньшей 1, по отношению к дуальным теориям с константой связи g много большей 1 [48] . Суперструнные теории связаны S-дуальностью следующим образом: суперструнная теория типа I S-дуальна гетеротической SO(32) теории, а теория типа IIB S-дуальна самой себе.
Существует также симметрия, связывающая преобразования S-дуальности и T-дуальности. Она называется U-дуальностью и наиболее часто встречается в контексте так называемых U-дуальных групп симметрии в М-теории, определённых на конкретных топологических пространствах. U-дуальность представляет собой объединение в этих пространствах S-дуальности и T-дуальности, которые, как можно показать на D-бране, не коммутируют друг с другом [50] .
Интригующим предсказанием теории струн является многомерность Вселенной. Ни теория Максвелла, ни теории Эйнштейна не дают такого предсказания, поскольку предполагают число измерений заданным (в теории относительности их четыре). Первым, кто добавил пятое измерение к эйнштейновским четырём, оказался немецкий математик Теодор Калуца (1919 год) [51] . Обоснование ненаблюдаемости пятого измерения (его компактности) было предложено шведским физиком Оскаром Клейном в1926 году [52] .
Требование согласованности теории струн с релятивистской инвариантностью (лоренц-инвариантностью) налагает жёсткие требования на размерность пространства-времени, в котором она формулируется. Теория бозонных струн может быть построена только в 26-мерном пространстве-времени, а суперструнные теории — в 10-мерном [17] .
Поскольку мы, согласно специальной теории относительности, существуем в четырёхмерном пространстве-времени [53] [54] , необходимо объяснить, почему остальные дополнительные измерения оказываются ненаблюдаемыми. В распоряжении теории струн имеется два таких механизма.
The first of these consists in the compactification of an additional 6 or 7 measurements, that is, their closure on themselves at such short distances that they cannot be detected in experiments. The six-dimensional model decomposition is achieved using Calabi-Yau spaces.
The classic analogy used when considering multidimensional space is a garden hose [55] . If you observe the hose from a far enough distance, it will seem that it has only one dimension - the length. But if you get closer to him, you find his second dimension - a circle. The true movement of an ant crawling along the surface of a hose is two-dimensional, but from a distance it will seem to us one-dimensional. Additional measurement is available for observation only from a relatively close distance; therefore, additional measurements of the Calabi-Yau space are available for observation only from an extremely close distance, that is, practically not detectable.
Another option - localization - is that the extra dimensions are not so small, but for a number of reasons all particles of our world are localized on a four-dimensional sheet in a multidimensional universe (multiverse) and cannot leave it. This four-dimensional sheet (brane) is the observable part of the multiverse. Since we, like all of our technology, consist of ordinary particles, we are in principle incapable of looking outside.
The only way to detect the presence of additional dimensions is gravity. Gravity, as a result of the curvature of space-time, is not localized on the brane, and therefore gravitons and microscopic black holes can go outside. In the observed world, such a process will look like a sudden disappearance of energy and impulse carried away by these objects.
String theory needs experimental verification, but none of the variations of the theory provide unambiguous predictions that could be tested in a critical experiment. Thus, string theory is still in its “embryonic stage”: it has many attractive mathematical features and can become extremely important in understanding the structure of the Universe, but further development is required in order to accept or reject it. Since string theory is unlikely to be verified in the foreseeable future due to technological limitations, some scientists doubt whether this theory deserves scientific status, since, in their opinion, it is not falsifiable in the Popper sense [12] [56] .
Of course, this in itself is not a reason to consider string theory wrong. Often, new theoretical constructions go through a stage of uncertainty, before, on the basis of comparison with the results of experiments, they are recognized or rejected (see, for example, Maxwell's equations [57] ). Therefore, in the case of string theory, either the development of the theory itself, that is, methods for calculating and drawing conclusions, or the development of experimental science for the study of previously inaccessible quantities is required.
In 2003, it became clear [58] that there are many ways to reduce 10-dimensional superstring theories to 4-dimensional effective field theory. The string theory itself did not provide a criterion by which it would be possible to determine which of the possible ways of reduction is preferable. Each of the options for reducing the 10-dimensional theory generates its own 4-dimensional world, which may resemble, or may differ from, the observed world. The entire set of possible implementations of the low-energy world from the original superstring theory is called the landscape of the theory.
It turns out that the number of such options is truly enormous. It is believed that their number is at least 10 100 , more likely - about 10 500 ; it is possible that their number is generally infinite [59] .
During 2005, it was repeatedly suggested [60] that progress in this direction can be associated with the inclusion of the anthropic principle [61] in this picture: man exists in such a Universe in which his existence is possible.
From a mathematical point of view, another problem is that, like quantum field theory, most string theory is still formulated perturbatively (in terms of perturbation theory) [62] . Despite the fact that nonperturbative methods have recently achieved significant progress, there is still no complete nonperturbative formulation of the theory.
As a result of experiments to detect "granularity" (degree of quantization) of space, which consisted in measuring the degree of polarization of gamma radiation coming from far away powerful sources, it turned out that the radiation of a gamma-ray burst GRB041219A, whose source is at a distance of 300 million light years, the grain of the space does not manifest itself up to the size of 10 −48 m, which is 10–14 times less than the Planck length [63] . This result is likely to force the external parameters of string theories to be revised [64] [65] [66] .
In 1996, string theorists Andrew Strominger and Kumrun Wafa, relying on the earlier results of Susskind and Sen, published the paper "The Microscopic Nature of Beckenstein and Hawking Entropy." In this work, Strominger and Wafé managed to use string theory to find the microscopic components of a certain class of black holes [67] , as well as to accurately calculate the contributions of these components to the entropy. The work was based on the application of a new method, partly beyond the perturbation theory, which was used in the 1980s and in the early 1990s. The result of the work coincided exactly with the predictions of Beckenstein and Hawking, made more than twenty years before.
Strominger and Wafa were opposed to real black hole formation processes by a constructive approach [2] . The bottom line is that they changed the point of view on the formation of black holes, showing that they can be constructed by painstakingly assembling into one mechanism an exact set of branes discovered during the second superstring revolution .
Strominger and Wafa were able to calculate the number of permutations of the microscopic components of a black hole, at which the total observed characteristics, such as mass and charge, remain unchanged. Then the entropy of this state is, by definition, equal to the logarithm of the number obtained - the number of possible microstates of the thermodynamic system. They then compared the result with the black hole event horizon area — this area is proportional to the black hole entropy, as predicted by Beckenstein and Hawking based on the classical understanding [2] —and obtained perfect agreement [68] . At least for the class of extreme black holes, Strominger and Wafa managed to find an application of string theory for analyzing microscopic components and accurately calculating the corresponding entropy.
This discovery turned out to be an important and convincing argument in support of string theory. The development of string theory still remains too rough for direct and accurate comparison with experimental results, for example, with measurements of the mass of quarks or electrons. String theory, however, provides the first fundamental rationale for the long-discovered property of black holes, the impossibility of explaining which has been hampered for many years by the research of physicists working with traditional theories. Even Sheldon Glashow, a Nobel laureate in physics and a staunch opponent of string theory in the 1980s, admitted in an interview in 1997 that “when string theorists talk about black holes, it’s almost an observable phenomenon, and this is impressive " [19] .
String cosmology is a relatively new and intensively developing area of theoretical physics, within which attempts are made to use the equations of string theory to solve some problems that arose in early cosmological theory. This approach was first used in the work of Gabriele Veneziano [69] , who showed how the inflationary model of the Universe can be obtained from the theory of superstrings. Inflation cosmology assumes the existence of a scalar field that induces inflationary expansion. In string cosmology, the so-called dilaton field [70] [71] is introduced instead, the quanta of which, unlike, for example, the electromagnetic field, are not massless, therefore the influence of this field is significant only at distances of the order of the size of elementary particles or at an early stage of the Universe [72] .
There are three main points in which string theory modifies the standard cosmological model. Firstly, in the spirit of modern research, which is increasingly clarifying the situation, it follows from string theory that the Universe should have a minimum allowable size. This conclusion changes the idea of the structure of the Universe directly at the moment of the Big Bang, for which the standard size of the Universe is obtained. Secondly, the concept of T-duality, that is, the duality of small and large radii (in its close connection with the existence of the minimum size) in string theory, is also important in cosmology [73] . Third, the number of space-time measurements in string theory is more than four, so cosmology must describe the evolution of all these dimensions. In general, a feature of string theory is that in it, apparently, the space-time geometry is not fundamental, but appears in the theory on a large scale or with weak coupling [74] .
Despite the fact that the arena of basic operations in string theory is not available to direct experimental study [75] [76] , a number of indirect predictions of string theory can still be verified in experiment [77] [78] [79] [80] .
First, the presence of supersymmetry is essential. It is expected that launched on September 10, 2008, but fully operational [81] which entered service in 2010, the Large Hadron Collider will be able to discover some supersymmetric particles. [13] This will be a strong support for string theory [19] .
Secondly, in models with the localization of the observable universe in the multiverse, the law of gravity of bodies changes at small distances. At present, a series of experiments are being carried out, verifying with high accuracy the law of world wideness at distances in hundredths of a millimeter [82] . Finding deviations from this law would be a key argument in favor of supersymmetric theories.
Third, in the same models, gravity can become very strong already on energy scales of the order of several TeV, which makes it possible to test it at the Large Hadron Collider. Currently, there is an active study of the processes of birth of gravitons and microscopic black holes in such variants of the theory.
Finally, some variants of string theory also lead to observational astrophysical predictions. Superstrings (cosmic strings), D-strings or other string objects stretched to intergalactic sizes have a strong gravitational field and can act as gravitational lenses.
In addition, moving strings should create gravitational waves, which, in principle, can be [83] found in experiments of the LIGO and VIRGO type.
They can also create small irregularities in relic radiation, which can be detected in future experiments [19] .
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String Theory and Superstrings
Terms: String Theory and Superstrings