STRING THEORY IN A NUTSHELL PDF
Request PDF on ResearchGate | On Jan 1, , Elias Kiritsis and others published String Theory in a Nutshell. String Theory in a Nutshell. To cite this article: Kostas Skenderis Class. Quantum Grav. 24 View the article online for updates and enhancements. Currently, string theory represents the only advanced approach to a .. "The novelty of the last couple of years, in a nutshell, is that we have learned that the.
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Chapter 1 A Brief Introduction Here we meet string theory for the ﬁrst time. We see how it ﬁts into the historical devel A First Course in String Theory. String Theory in a Nutshell. 1. 1 What Is String Theory? 3. I break the laws of comedy by giving away my punch lines about what string theory is; what the leading. The Case for String Theory. 3. A Stringy Historical Perspective. 6. Conventions. 8. Bibliography. 9. 2 Classical String Theory. The Point Parade.
M-theory is a theory in physics that unifies all consistent versions of superstring theory. The existence of such a theory was first conjectured by Edward Witten at a string theory conference at the University of Southern California in the Spring of Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories appeared, at first, to be very different, work by several physicists showed that the theories were related in intricate and nontrivial ways.
Living Rev. Cook, P. Connections between Kac—Moody algebras and M-theory. Pioline, B.: Rozali, M.: Comments on Background Independence and Gauge Redundancies.
McAllister, L. String Cosmology: A Review. Hollands, S. Gasperini M.: Elements of String Cosmology. Brandenberger, R.: String Gas Cosmology. Cornalba L. Time-dependent orbifolds and string cosmology. Berkooz, M. Craps, B.: Big Bang Models in String Theory. Craps, B. A Matrix Big Bang. Blau M. DLCQ and plane wave matrix big bang models. JHEP , arXiv: Stringy model of cosmological dark energy.
AIP Conf. The claim is that this quantum field theory is equivalent to the gravitational theory on the bulk anti-de Sitter space in the sense that there is a "dictionary" for translating entities and calculations in one theory into their counterparts in the other theory.
String theory as a theory of quantum gravity: a status report
For example, a single particle in the gravitational theory might correspond to some collection of particles in the boundary theory. In addition, the predictions in the two theories are quantitatively identical so that if two particles have a 40 percent chance of colliding in the gravitational theory, then the corresponding collections in the boundary theory would also have a 40 percent chance of colliding.
In this example, the spacetime of the gravitational theory is effectively seven-dimensional hence the notation AdS 7 , and there are four additional " compact " dimensions encoded by the S 4 factor. In the real world, spacetime is four-dimensional, at least macroscopically, so this version of the correspondence does not provide a realistic model of gravity. Likewise, the dual theory is not a viable model of any real-world system since it describes a world with six spacetime dimensions.
Nevertheless, the 2,0 -theory has proven to be important for studying the general properties of quantum field theories. Indeed, this theory subsumes many mathematically interesting effective quantum field theories and points to new dualities relating these theories. For example, Luis Alday, Davide Gaiotto, and Yuji Tachikawa showed that by compactifying this theory on a surface , one obtains a four-dimensional quantum field theory, and there is a duality known as the AGT correspondence which relates the physics of this theory to certain physical concepts associated with the surface itself.
In addition to its applications in quantum field theory, the 2,0 -theory has spawned important results in pure mathematics. For example, the existence of the 2,0 -theory was used by Witten to give a "physical" explanation for a conjectural relationship in mathematics called the geometric Langlands correspondence.
In this version of the correspondence, seven of the dimensions of M-theory are curled up, leaving four non-compact dimensions. Since the spacetime of our universe is four-dimensional, this version of the correspondence provides a somewhat more realistic description of gravity.
The ABJM theory appearing in this version of the correspondence is also interesting for a variety of reasons. Introduced by Aharony, Bergman, Jafferis, and Maldacena, it is closely related to another quantum field theory called Chern—Simons theory.
The latter theory was popularized by Witten in the late s because of its applications to knot theory.
In addition to being an idea of considerable theoretical interest, M-theory provides a framework for constructing models of real world physics that combine general relativity with the standard model of particle physics.
Phenomenology is the branch of theoretical physics in which physicists construct realistic models of nature from more abstract theoretical ideas. String phenomenology is the part of string theory that attempts to construct realistic models of particle physics based on string and M-theory. Typically, such models are based on the idea of compactification. By choosing this shape appropriately, they can construct models roughly similar to the standard model of particle physics, together with additional undiscovered particles,  usually supersymmetric partners to analogues of known particles.
One popular way of deriving realistic physics from string theory is to start with the heterotic theory in ten dimensions and assume that the six extra dimensions of spacetime are shaped like a six-dimensional Calabi—Yau manifold. This is a special kind of geometric object named after mathematicians Eugenio Calabi and Shing-Tung Yau. Other similar methods can be used to construct models with physics resembling to some extent that of our four-dimensional world based on M-theory.
Partly because of theoretical and mathematical difficulties and partly because of the extremely high energies beyond what is technologically possible for the foreseeable future needed to test these theories experimentally, there is so far no experimental evidence that would unambiguously point to any of these models being a correct fundamental description of nature. This has led some in the community to criticize these approaches to unification and question the value of continued research on these problems.
In one approach to M-theory phenomenology, theorists assume that the seven extra dimensions of M-theory are shaped like a G 2 manifold. This is a special kind of seven-dimensional shape constructed by mathematician Dominic Joyce of the University of Oxford. For example, physicists and mathematicians often assume that space has a mathematical property called smoothness , but this property cannot be assumed in the case of a G 2 manifold if one wishes to recover the physics of our four-dimensional world.
Another problem is that G 2 manifolds are not complex manifolds , so theorists are unable to use tools from the branch of mathematics known as complex analysis. Finally, there are many open questions about the existence, uniqueness, and other mathematical properties of G 2 manifolds, and mathematicians lack a systematic way of searching for these manifolds. Because of the difficulties with G 2 manifolds, most attempts to construct realistic theories of physics based on M-theory have taken a more indirect approach to compactifying eleven-dimensional spacetime.
In this approach, one imagines that one of the eleven dimensions of M-theory is shaped like a circle. If this circle is very small, then the spacetime becomes effectively ten-dimensional. One then assumes that six of the ten dimensions form a Calabi—Yau manifold. If this Calabi—Yau manifold is also taken to be small, one is left with a theory in four-dimensions. Heterotic M-theory has been used to construct models of brane cosmology in which the observable universe is thought to exist on a brane in a higher dimensional ambient space.
It has also spawned alternative theories of the early universe that do not rely on the theory of cosmic inflation.
String theory in a nutshell
From Wikipedia, the free encyclopedia. For a more accessible and less technical introduction to this topic, see Introduction to M-theory. Framework of superstring theory.
Related concepts. Verlinde H. Verlinde Witten Yau Zaslow. Main articles: Quantum gravity and String theory. Extra dimensions and Compactification physics. S-duality and T-duality. Main article: History of string theory. Kaluza—Klein theory. Second superstring revolution. Matrix theory physics. Noncommutative geometry and Noncommutative quantum field theory. ABJM superconformal field theory. String phenomenology. See Wald , p.
See Zee , p. See Randall and Sundrum Journal of High Energy Physics. Letters in Mathematical Physics. A conjecture".
Physical Review D. String theory and M-theory: A modern introduction. Cambridge University Press. Physics Letters B. Nuclear Physics B. Connes, Alain Noncommutative Geometry. Academic Press. Communications in Mathematical Physics. Dine, Michael Strings, Branes and Gravity. Dirac, Paul Proceedings of the Royal Society of London. Mathematical and Physical Sciences. Duff, Michael International Journal of Modern Physics A.
Scientific American. Advances in Mathematics. Greene, Brian The Elegant Universe: Random House. Griffiths, David Introduction to Quantum Mechanics. Pearson Prentice Hall.
[PDF] String Theory in a Nutshell Read Online - video dailymotion
Hull, Chris; Townsend, Paul Khovanov, Mikhail Duke Mathematical Journal. Klebanov, Igor; Maldacena, Juan Physics Today. Archived from the original on CS1 maint: Advances in Theoretical and Mathematical Physics. Maldacena, Juan Moore, Gregory Notices of the AMS. Retrieved 6 August Retrieved 14 August Because of the speculative nature of quantum-gravity research, there is much debate as to the correct implementation of background independence.
Ultimately, the answer is to be decided by experiment, but until experiments can probe quantum-gravity phenomena, physicists have to settle for debate. Below is a brief summary of the two largest quantum-gravity approaches. Physicists have studied models of 3D quantum gravity, which is a much simpler problem than 4D quantum gravity this is because in 3D, quantum gravity has no local degrees of freedom. In these models, there are non-zero transition amplitudes between two different topologies,  or in other words, the topology changes.
This and other similar results lead physicists to believe that any consistent quantum theory of gravity should include topology change as a dynamical process.
String theory is usually formulated with perturbation theory around a fixed background. While it is possible that the theory defined this way is locally background-invariant, if so, it is not manifest, and it is not clear what the exact meaning is.
One attempt to formulate string theory in a manifestly background-independent fashion is string field theory , but little progress has been made in understanding it. If so, this could describe a kind of superselection sector of the putative background-independent theory. But it would be still restricted to anti-de Sitter space asymptotics, which disagrees with the current observations of our Universe.
A full non-perturbative definition of the theory in arbitrary spacetime backgrounds is still lacking. Topology change is an established process in string theory.
A very different approach to quantum gravity called loop quantum gravity is fully non-perturbative, manifest background-independent: From Wikipedia, the free encyclopedia.
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