Abstract: Despite the lack of experimental confirmation and of unambiguous theoretical proof, superstring theory has long been considered by many the only consistent quantized theory of gravity and the unique viable framework for the unification of all fundamental forces of nature. In the first part of this essay I explore the type of reasoning used to support such statements. In order to illustrate the argument, in the second part I focus on one of the most acclaimed achievements of the theory: the AdS/CFT correspondence. Finally, I conclude by observing that what constitutes a result in superstring theory involves more than purely theoretical arguments. Specifically, the acceptance of facts in superstring theory is inextricably linked to the large group of people that make it possible, whether they are string practitioners or not.

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SELECTED READINGS FOR ESSAY 1 (I)

SELECTED READINGS FOR ESSAY 1 (I)

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The evolving scientific status of string theory results

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Trying to overcome the impasse with what a massless particle with spin two meant for the dual model of strong nuclear interactions, in 1974 Joël Scherk and John Schwarz proposed a reinterpretation of this particle as the quantum carrier of gravitational force: ‘‘The possibility of describing particles other than hadrons (leptons, photons, gauge bosons, gravitons, etc.) by a dual model is explored. The Virasoro-Shapiro model is studied first, interpreting the massless spin-two state of the model as a graviton.’’[source] In their seminal paper Scherk and Schwarz showed that consistency of the dual model entailed a higher dimensional version of the Hilbert action. From this it then followed that the model included gravitational forces as described by Einstein’s equation. These were the primary motives driving the authors to propose that string theory quantized gravity: the spectrum showed a massless spin-2 particle, and, moreover, a ten-dimensional Einstein equation could be derived. In those days many theoretical physicists found these two results too weak to allege that a quantized theory of gravity had been achieved. This explains the cautious reception the theory received in its early years. Unexpectedly, however, this once feeble proposal has become widely established within theoretical physics, even though the mathematical support has remained almost unchanged for more than thirty years. Let us comment further on this.

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In the last chapter of a classic string theory graduate textbook written in 1989, here is how the quantization of gravity is presented:

String theory is claimed to be a unifying framework for the description of all particles and their interactions, including gravity. However, up to now our exposition of the subject was rather formal and it is not at all transparent how it can be relevant for low energy phenomenology. The only hint we got so far was from looking at the spectrum. There especially the occurrence of a spin two tensor particle indicated that gravity might be contained in string theory.[source]*******You can read this blog for free! Please, do not copy its content.*******

Note that this observation is relegated to the last part of the book, after some three hundred pages of mathematical details. No doubt this is a queer situation. Why leave the most important argument in favour of the theory, at least in popular accounts and undergraduate level materials, to the final pages of the textbook? The answer to this question is provided by the cautious words of the authors. Even more surprising is that the same argument has been used for decades. The only difference is that nowadays the quantization of gravity is not considered an ‘‘elusive task,’’ as many string theoreticians used to say, but rather an accomplished one. For example, in the midst of what string theorists consider the second major revolution of the field, Edward Witten wrote in Physics Today: ‘‘Moreover, these theories have (or this one theory has) the remarkable property of predicting gravity ― that is, of requiring the existence of a massless spin-2 particle whose coupling at long distances are those of general relativity.’’ [source] (Italics in the original.) And in an up to date textbook, aimed at undergraduate physics students, the author says: ‘‘The striking quantum emergence of gravitation in string theory has the full flavor of a prediction.’’ [source] Understandably, declarations of this kind have given rise to hot discussions among supporters and detractors of the theory. The question is: what happened in those intervening years? Why are string theorists so optimistic now? Did they really find an unquestionable proof, experimental or theoretical, that their theory quantizes gravity?

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In point of fact, to this day nobody has presented an entirely convincing proof of this. For some theoretical physicists, the presence of a massless spin-2 particle in its spectrum is not enough to a quantized theory of gravity. I is also argued that the low energy limit analysis of superstring theory does not imply that that particle is the graviton. The former string theorist Daniel Friedan, one of the early major contributors, is emphatic about this:

In particular, there is no justification for the claim that string theory explains or predicts gravity. String theory gives perturbative scattering amplitudes of gravitons. Gravitons have never been observed. Gravity in the real world is accurately described by general relativity, which is a classical field theory. There is no derivation of general relativity from string theory. … String theory does not produce any mechanical theory of gravity, much less a quantum mechanical theory.[source]*******You can read this blog for free! Please, do not copy its content.*******

Why then do practitioners believe that ‘‘string theory is a quantum theory, and, because it includes gravitation, it is a quantum theory of gravity’’? How have string theorists arrived at the conclusion that ‘‘the harmonious union of general relativity and quantum mechanics is a major success’’[source] of superstrings? Moreover, how have they managed to convince other theoreticians of the validity of their explanations? Let us look at another example.

In the abovementioned paper, Scherk and Schwarz also declared that string theory could unify all the fundamental interactions: ‘‘If it is, a scheme of this sort might provide a unified theory of weak, electromagnetic, and gravitational interactions.’’[source] (These known interactions were then complemented with the strong nuclear force, the latter successfully described by quantum chromodynamics.) This was in 1974. Years later, and after intense work, the proposal had still not been proved. The four-dimensional standard model (it exludes gravity), with all its details, could not be deduced from string theory. In a lecture given at the International Centre for Theoretical Physics (ICTP) in 1986, one of the leading string phenomenologists of the time stated: ‘‘Being defined in d=10, some compactification of the six dimensions would be required to make contact with phenomenology. This process is at the moment not understood at all; one has to make crude approximations and then check for consistency a posteriori.’’ [source] The reason why the process of superstring compactification ‘‘was not understood at all’’ is due to the stringent constrains that supersymmetry imposes on the four dimensional model. As expected from the standard model of particle physics, any physical result with supersymmetry must be renormalizable and requires the existence of chiral spinors . However, there are some difficulties with this: firstly, supergravity with one supersymmetry is not renormalizable, and, secondly, models with higher numbers of supersymmetries do not include chiral spinors. Satisfying these two conditions is the difficult mission assigned to string phenomenologists. There are several approaches to the problem: the simplest model considers compactification on a multi-dimensional torus, other string theorists prefer to use constructs known as orbifolds or orientifolds; more recently G2 manifolds were tested. Other Calabi-Yau manifolds are currently under examination. Despite this confusing situation, there is one thing string theorists know they must answer: ‘‘Why do we live on this particular string vacuum or SSC [superstring compactification]?’’[source] This is the most urgent question that needs to be addressed in order to make contact with physical reality. As Michio Kaku writes in the introduction to the 2000 edition of his textbook on elementary string theory: ‘‘The search for the true vacuum of string theory is therefore the central theme of this book.’’[source] So, if we could explain why the universe chose this particular vacuum we would be able to understand how the standard model arises from superstring theory and why the universe expands as it does. It has been argued by critics that this reformulation of the problem does not solve it. On the contrary, it makes it harder and moves it, dangerously, towards the realm of theology.

In this case, as in the previous case of the quantization of gravity, superstring theorists have been unable to offer an accurate and comprehensive explanation of four-dimensional physics. To be sure, string phenomenology, from the old heterotic string to recent brane models, does not provide the correct value for the quantities associated to the elementary particles known so far. In addition to this, critics emphasize, it does not answer crucial questions that intrigue particle physicists: how is the electroweak symmetry broken? what fixes the masses of the Higgs boson, quarks, neutrinos and charged leptons? what are the sources of the cold dark matter? what produced the big bang? why is there matter-antimatter asymmetry? This state of affairs has lead Sheldom Glashow, an eminent particle physicist, to declare that string theory ‘‘has failed in its primary goal, which is to incorporate what we already know into a consistent theory that explains gravity as well. The new theory must incorporate the old theory and say something more. String theory has not succeeded in this fashion.’’[source]

From the previous examples we have learnt some important things about the development of string theory. Firstly, as research progresses in a given topic, an explicit reference to the unsolved problem tends to disappear from the literature. For instance, we saw how the quantization of gravity is considered by string theorists to be an accomplished task that does not deserve further study, or even a mention. Secondly, while research advances, the initial problem changes in such a way that it becomes increasingly difficult to unravel the convoluted relationship connecting the final problem to the original one. This was illustrated by our second example concerning string theory and the unification of the forces. Originally the idea was to extract the standard model from superstring theory, an investigation encouraged during the second half of the eighties by the promising results obtained from the heterotic string. Then, by the mid-nineties, the goal was to determine the unique vacuum of the mother of all the theories, the M-Theory. And, more recently, the focus was on the right ‘‘environment’’ of the anthropic solution. Things have changed, but the fundamental query remains unsolved: how do we get the standard model from string theory? With these examples we have learnt something else: this occurs while an ‘‘outward’’ discourse (from the ‘‘inside’’ to the ‘‘outside’’ of the professional community) proclaims that the theory has solved such problems. Indeed, in this movement disadvantages have been transmuted into virtues.

In spite of these fundamental flaws in the theory, enthusiasts proclaim that ‘‘in string theory all forces are truly unified in a deep and significant way,’’ or, a bit more prudently, ‘‘string theory leads in a remarkably simple way to a reasonable rough draft of particle physics unified with gravity.’’[source] The final outcome of this discourse is the same: the stabilization of string theory as a quantized theory of gravity and unified model. Before concluding this introduction, I would like to add two more quotations. In Zwiebach’s undergraduate textbook he asks:

Why is string theory truly a unified theory? The reason is simple and goes to the heart of the theory. In string theory, each particle is identified as a particular vibrational mode of an elementary microscopic string.[source]

Thus, string theory is a unified theory thanks to its extreme reductionist approach. Brian Greene, in his best-selling book, backs up this statement. Years of hard work have shown that the reductionist approach to string theory is correct.

These works showed conclusively that numerous features of the standard model ― features that had been painstakingly discovered over the course of decades of research ― emerged naturally and simply from the grand structure of string theory.[source]

I think what we have seen in these examples is a characteristic of string theory research and its elaboration of physical reality. At first, a hypothesis is made, explaining openly its significance as well as its difficulties. At this stage no one is sure of the real value of the conjecture, however, it is interesting enough to drive a significant part of the physics community to devote itself to its development. Step by step ‘‘evidence’’ accumulates and after a while the string theory fact emerges. String theorists have created in this way their own nature: a supersymmetric world, a big bang with all the fundamental forces combined, a multi-dimensional universe, and so forth. Although I have provided support to this thesis in the case of the two sanctioned ‘‘achievements’’ of superstring theory, quantization of gravity and unification of the fundamental forces, I will now illustrate in full detail this complex process with another ground-breaking proposal: the AdS/CFT correspondence.

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SELECTED READINGS FOR ESSAY 1 (I)

SELECTED READINGS FOR ESSAY 1 (I)

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