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Introduction to String Theory

Scattered off String Theory

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String Theory
Stringinteractions
All Roads Lead to String Theory (Polchinski)
Prior to the First Superstring Revolution
Early History S-Matrix Theory
Regge Trajectory
Bosonic String Theory Worldsheet
String
Bosonic String Theory
String Perturbation Theory
Tachyon Condensation
Supersymmetric Revolution Supersymmetry
RNS Formalism
GS Formalism
BPS
Superstring Revolutions
First Superstring Revolution GSO Projection
Type II String Theory
Type IIB String Theory
Type IIA String Theory
Type I String Theory
Type H String Theory
Type HO String Theory
Type HE String Theory
Second Superstring Revolution T-Duality
D-Brane
S-Duality
Horava-Witten String Theory
M-Theory
Holographic Principle
N=4 Super-Yang-Mills Theory
AdS CFT
BFSS Matrix Theory
Matrix String Theory
(2,0) Theory
Twistor String Theory
F-Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
Phenomenology String Theory Landscape
Minimal Supersymmetric Standard Model
String Phenomenology


String Theory is basically a theory that postulates that all particles are really extended objects. In the old, canonical String Theories, these extended objects are Strings. The vibrational modes of these strings determine the properties of the emergent particle. The rotational modes of these strings determine the Spin in the RNS Formalism.

ImportanceEdit this section

Currently, String Theory is studied because it is a suitable candidate for a Theory of Everything. In other words, it can describe all interactions, and matter, using a simple gauge group or a square of a simple gauge group. It also allows for a Quantised version of General Relativity, and thus a theory of Quantum Gravity. Of course, every Theory of Everything is by definition also a theory of Quantum Gravity (but not vice versa).

OverviewEdit this section

Bosonic String TheoryEdit this section

Bosonic String Theory is the earliest version of String Theory. It can be written easily by describing a number of strings, suspended, interacting, in the background Spacetime. It has two major issues:

  1. The lack of fermions in the spectrum.
  2. The presence of a Tachyon in the spectrum.

SupersymmetryEdit this section

Supersymmetry is a symmetry that can be incorporated in String Theory to allow the existence of fermions. It is attractive for other reasons, too. For example, it allows the existence of spin-3/2 particles, which would otherwise not be existent if there were no Supersymmetry, leaving a hole in the Spin spectrum.

RNS FormalismEdit this section

The RNS Formalism is a formalism for introducing Supersymmetry in String Theory. It has intrinsic Worldsheet Supersymmetry. It, however, still has a Tachyon in it's spectrum. This can be eliminated through a GSO Projection.

GS FormalismEdit this section

The GS Formalism is yet another formalism for introducing Supersymmetry in String Theory. It has intrinsic Spacetime Supersymmetry. It has no Tachyon.

Type II StringsEdit this section

Type II String Theory is the easiest String Theory to understand from the RNS Formalism. There are two Type II String Theoryies; The non-chiral Type IIB String Theory,; and the chiral Type IIA String Theory.

Type I StringsEdit this section

Type I String Theory is the orientifold projection of Type IIB String Theory, but combined with Open String sectors.

Type H StringsEdit this section

Type H String Theory is a hybrid of Bosonic String Theory and Type II String Theory. It comes in two forms; Type HO String Theory,; and Type HE String Theory. The latter is likely to be capable of describing our universe correctly due to its gauge group being capable of embedding the Standard Model gauge group as a Subgroup.

Dualities and D-BranesEdit this section

The Second Superstring Revolution is well-known for having given rise to D-Branes and Dualities between String Theoryies. These discoveries hint towards the existence of a new theory, called M-Theory.

Holography, AdS/CFT, and Matrix TheoryEdit this section

A key discovery in the way to non-perturbative String Theory, is Holography, a principle that states that information within a region is completely encoded onto it's boundary in a different way. A special case of this is AdS/CFT, which states that a String Theory in Anti-de-Sitter Space is equivalent to the Conformal Field Theory on it's conformal boundary.

An application of AdS CFT is BFSS Matrix Theory. It gives us a fully non-perturbative formulation of M-Theory, but only in Anti-de-Sitter Space. BFSS Matrix Theory is an example of a "Matrix Model".

Another application is Matrix String Theory. It is a "Matrix Model" for Type IIA String Theory and Type HE String Theory.

F-TheoryEdit this section

F-Theory is an interesting formulation of Type IIB String Theory.

Twistor String TheoryEdit this section

Twistor String Theory is String Theory in Twistor Space. It is equivalent to perturbative Yang-Mills Theory.

String Field TheoryEdit this section

String Field Theory is a formulation of String Theory in the language of Quantum Field Theory. See [1], which is also mirrored at [2].

Berkovitis FormalismEdit this section

The Berkovitis Formalism, also known as the Pure Spinor Formalism, is a way of formulating Super String Theory in a way similiar to the GS Formalism. See [3].

MSSMEdit this section

The MSSM is a Supersymmetric extensionp to the Standard Model. When in the vacua of M-Theory, it predicts a Higgs Mass that concurs with experiments [4].

String PhenomenologyEdit this section

String Phenomenology refers to finding the predictions of String Theory that can be tested in the real world.

HistoryEdit this section

Historical MotivationEdit this section

(1961 to 1968)Edit this section

The Historical Motivation behind String Theory was that it would probably describe hadrons. However, it was found to be an incorrect theory, as it predicted only bosons, and predicted a Tachyon. This early version of String Theory is called Bosonic String Theory.

Quantum Chromodynamics, instead, became the "correct" theory of hadrons. String Theory was for the most part, discarded by many physicists.

StringsEdit this section

(1969)Edit this section

When String Theory was initially discovered, it was S-Matrix Theory. It was all about S-Matrices, Regge Trajectories, and all that; but there was no concept of Strings involved. With the discovery of the Nambu-Goto Action by Yoichiro Nambu and Tetsou Goto, it became clear that String Theory was a theory of Strings. This was actually a follow-up to the discovery of Strings by Leonard Susskind, Holger Biech Nielson, and Yoichiro Nambu. This action was later expanded/modified into the Polyakov Action by Brink, Di Vecchia, Howe, and Tucker. This became known as the Polyakov Action when Alexander Polyakov included it in one of his textbooks.

Supersymmetric RevolutionEdit this section

(1970-1981)Edit this section

Pierre Ramond discovered Supersymmetry, to be specific, Worldsheet Supersymmetry. He discovered that adding spacetime vectors as "fermionic fields" allows the arisal of fermions in String Theory. This can be seen from the RNS Action, with certain elegant Supersymmetryic transformation invariance.

However, Pierre Ramond worked only with periodic boundary conditions for the fermionic fields. Meanwhile, inspired by this work, Andre Neveu, and John Schwarz worked with anti-periodic boundary conditions.

All this eventually lead to the discovery of the RNS Formalism; when it was eventually realised that the work by Pierre Ramond was compatible with the work by Andre Neveu and John Schwarz.

This was followed by the discovery of the GS Formalism by Michael Green and John Schwarz. This formalism had explicit Spacetime Supersymmetry.

The RNS Formalism, however, had the problem of a Tachyon in it's ground state, signifying an unsthable Spacetime (as shown by Ashok Sen. This problem was absent in the GS Formalism, however.

Alexander Polyakov gave it a Path Integral Formulation. Meanwhile, Michael Green and John Schwarz discovered T-Duality for Bosonic Strings.

First Superstring RevolutionEdit this section

(1981-1989)Edit this section

The First Superstring Revolution was a period during which various discoveries were made, including the GSO Projection, and the discovery of the 5 consistent Superstring Theoryies.

Michael Green, Joel Scherk, and David Olive discovered the GSO Projection which maps out the Tachyon from the RNS Formalism.

In the same paper, they found that there are 2 ways to apply the GSO Projection; one that preserves Chirality, and one that doesn't.

Augusto Sagnotti discovered Type I String Theory as a Non-Oriented Theory containing both Open Strings and Closed Strings/.

David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm discovered the two Type H String Theoryies, namely, the Type HO String Theory and the Type HE String Theory.

Meanwhile, Vipul Periwal showed that String Perturbation Theory is divergent.

Second Superstring RevolutionEdit this section

(1990-1998)Edit this section

Joseph Polchinski showed that D-Branes were necessary in String Theory.

Edward Witten discovered that the Type IIA String Theory was T-Dual to the Type IIB String Theory, the Type HE String Theory was T-Dual to the Type HO String Theory, and that the Type IIB String Theory displayed self-S-Duality, whereas the Type I String Theory was S-Dual to the Type HO String Theory.

Petr Horava and Edward Witten discovered the Horava-Witten String Theory (the S-Dual to the Type HE String Theory).

Various physicists, including Edward Witten, Ashok Sen, Nathan Seiberg, etc., postulated (see for example, [5], [6] [7]) that these two String Theoryies are actually a \new theory, which came to be known as M-Theory compactified on a circle, and a line segment, respectively. This is also when Michael Duff coined the term "The Theory Formerly known as Strings" [8].

Thomas Banks, Willy Fischler, Stephen Shenker, and Leonard Susskind discovered BFSS Matrix Theory [9] , after which Lubos Motl discovered Matrix String Theory [10] [11] [12] [13] [14].

The Phenomenological and Experimental EraEdit this section

(2000-present)Edit this section

This is the era in which there were significant achievements in String Phenomenology.

Piyush Kumar, Bobby Acharya, and Gordon Kane discovered that the MSSM lies in the realistic portion of the landscape of M-Theory. Since the MSSM predicts a Higgs Mass of 125 GeV/c02, so do the realistic vacua of M-Theory. This concurs with experiments. [4]. This Phenomenological Achievement provides compelling evidence for String Theory.

Additionally, numerous experiments have been conducted at CERN to test String Theory. Certain results seem to concur with the predictions of String Theory. c.f. [15] [16] [17] [18][19] [[20] [21]].

There have also been certain experimental results which do not exactly completely agree with the predictions of String Theory, specifically for extra dimensions, such as [22]. It is to be noted, however, that these results do not rule out compactification lengths smaller than half a milimetre.

Experimental TestsEdit this section

Of SupersymmetryEdit this section

Between 2000 and present, there were significant achievements in String Phenomenology, which gives us results that String Theory predicts, helping us test it.

Piyush Kumar, Bobby Acharya, and Gordon Kane discovered that the MSSM lies in the realistic portion of the landscape of M-Theory. Since the MSSM predicts a Higgs Mass of 125 GeV/c02, so do the realistic vacua of M-Theory. This concurs with experiments. [4]. This Phenomenological Achievement provides compelling evidence for String Theory.

Additionally, numerous experiments have been conducted at CERN to test String Theory. Certain results seem to concur with the predictions of String Theory. c.f. [23] [24] [25] [26][27][28] [29].

Of Extra DimensionsEdit this section

There have also been certain experimental results which do not exactly completely agree with the predictions of String Theory, specifically for extra dimensions, such as [30]. It is to be noted, however, that these results do not rule out compactification lengths smaller than half a milimetre.

ApplicationsEdit this section

In Condensed Matter PhysicsEdit this section

AdS/CMT is a correspondence between String Theory and Condensed Matter Physics.

String Net Theory is an application of String Theory in Condensed Matter Physics.

In Quantum Field TheoryEdit this section

AdS/CFT tells us that certain weakly-coupled String Theoryies are equivalyent to certain strongly-coupled Quantum Field Theoryies. This allows us to use Perturbative Techniques\ to study strongly-coupled Quantum Field Theoryies.


ReferencesEdit this section

  1. Siegel, W. http://insti.physics.sunysb.edu/~siegel/sft.pdf
  2. Siegel, W. http://arxiv.org/pdf/hep-th/0107094v1.pdf
  3. http://motls.blogspot.in/2005/01/pure-spinor-formalism.html
  4. 4.0 4.1 4.2 Acharya, Bob; Kumar, P., Kane, G. (12/4/2012). "Compactified String Theories -- Generic Predictions for Particle Physics". International Journal of Modern Physics. 2012 27 (9): 1–30. doi:10.1142/S0217751X12300128. http://arxiv.org/abs/1204.2795. Retrieved 13 July 2013.
  5. Witten, Edward (1996). "Five-Branes and M-Theory on an orbifold". Nucl.Phys.B 463 (6): 382-397. http://arxiv.org/pdf/hep-th/9512219v3.pdf.
  6. Sen, Ashok (1996). "Unification of String Dualities". Nucl.Phys.Proc.Suppl. 58 (6): 5-19. http://arxiv.org/pdf/hep-th/9609176.pdf.
  7. Townsend, Paul (1996). "Brane Surgery". Nucl.Phys.Proc.Suppl. 58 (6): 163-175. http://arxiv.org/pdf/hep-th/9512219v3.pdf.
  8. Duff, Michael. "The Theory Formerly known as Strings". http://arxiv.org/pdf/hep-th/9608117v3.pdf.
  9. Banks, Tom; Ficshler, Willy., Shenker, Stephen., Susskind, Leonard. (1996). "M Theory as a Matrix Model: A Conjecture". Physical Review D.```~~~```. 1997 55 (8): 5112-5228. doi:10.1103/PhysRevD.55.5112. http://arxiv.org/pdf/hep-th/9610043v3.pdf.
  10. Motl, Lubos; Banks, Thomas. (2001). "Nonperturbative Formulations of Superstring Theory". New Brunswick Rutgers, The State University of New Jersey. http://arxiv.org/pdf/hep-th/0109149.pdf.
  11. Motl, Lubos; Susskind, Leonard. (1997). "Finite N Heterotic Matrix Models and Discrete Light Cone Quantization". ArXiV. http://arxiv.org/pdf/hep-th/9708083v2.pdf.
  12. Motl, Lubos; Banks, Thomas. (1997). "Heterotic Strings from Matrices". Journal of High Energy Physics 9712 (4). http://arxiv.org/pdf/hep-th/9703218v1.pdf.
  13. Motl, Lubos (1997). "Proposals on nonperturbative superstring interactions". ArXiV. http://arxiv.org/pdf/hep-th/9701025v3.pdf.
  14. Motl, Lubos (1997). "Quaternions and M(atrix) theory in spaces with boundaries". ArXiV. http://arxiv.org/pdf/hep-th/9612198v3.pdf.
  15. http://motls.blogspot.in/2013/09/cms-25-sigma-excess-in-tophiggs.html
  16. http://motls.blogspot.in/2013/10/cms-second-beh-boson-near-135gev-gets.html
  17. http://motls.blogspot.in/2013/09/cms-3-sigma-deficits-in-search-for.html
  18. http://motls.blogspot.com/2013/08/two-sigmaish-cms-multilepton-excesses.html
  19. Akula, Sujeet.; Nath, Pran., Feldman, Daniel. Peim, Gregory.. "Excess Observed in CDF B_s^0\to\mu^+\mu^- and SUSY at the LHC". Physics Review D..
  20. http://www.lpta.univ-montp2.fr/article.php3?id_article=316
  21. http://arxiv.org/pdf/astro-ph/0609189.pdf
  22. Hoyle, C. D.; Schmidt, U., Heckel, B.R., Adelberger, E.G., Gundlach, J.H., Kapner, D.J./, Swanson, H.E. (2001). "Sub-millimeter tests of the gravitational inverse-square law: A search for "large" extra dimensions". Physical Review Letters 86: 1418-1421. http://arxiv.org/pdf/hep-ph/0011014v1.pdf.
  23. http://motls.blogspot.in/2013/09/cms-25-sigma-excess-in-tophiggs.html
  24. http://motls.blogspot.in/2013/10/cms-second-beh-boson-near-135gev-gets.html
  25. http://motls.blogspot.in/2013/09/cms-3-sigma-deficits-in-search-for.html
  26. http://motls.blogspot.com/2013/08/two-sigmaish-cms-multilepton-excesses.html
  27. Akula, Sujeet.; Nath, Pran., Feldman, Daniel. Peim, Gregory.. "Excess Observed in CDF B_s^0\to\mu^+\mu^- and SUSY at the LHC". Physics Review D..
  28. http://www.lpta.univ-montp2.fr/article.php3?id_article=316
  29. http://arxiv.org/pdf/astro-ph/0609189.pdf
  30. Hoyle, C. D.; Schmidt, U., Heckel, B.R., Adelberger, E.G., Gundlach, J.H., Kapner, D.J./, Swanson, H.E. (2001). "Sub-millimeter tests of the gravitational inverse-square law: A search for "large" extra dimensions". Physical Review Letters 86: 1418-1421. http://arxiv.org/pdf/hep-ph/0011014v1.pdf.

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