String Theory  

All Roads Lead to String Theory (Polchinski)  
Prior to the First Superstring Revolution
 
Early History  SMatrix 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  TDuality DBrane SDuality HoravaWitten String Theory MTheory Holographic Principle N=4 SuperYangMills Theory AdS CFT BFSS Matrix Theory Matrix String Theory (2,0) Theory Twistor String Theory FTheory 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.
Table of Contents
 1 Importance
 2 Overview
 2.1 Bosonic String Theory
 2.2 Supersymmetry
 2.3 RNS Formalism
 2.4 GS Formalism
 2.5 Type II Strings
 2.6 Type I Strings
 2.7 Type H Strings
 2.8 Dualities and DBranes
 2.9 Holography, AdS/CFT, and Matrix Theory
 2.10 FTheory
 2.11 Twistor String Theory
 2.12 String Field Theory
 2.13 Berkovitis Formalism
 2.14 MSSM
 2.15 String Phenomenology
 3 History
 4 Experimental Tests
 5 Applications
 6 References
Importance
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).
Overview
Bosonic String Theory
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:
 The lack of fermions in the spectrum.
 The presence of a Tachyon in the spectrum.
Supersymmetry
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 spin3/2 particles, which would otherwise not be existent if there were no Supersymmetry, leaving a hole in the Spin spectrum.
RNS Formalism
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 Formalism
The GS Formalism is yet another formalism for introducing Supersymmetry in String Theory. It has intrinsic Spacetime Supersymmetry. It has no Tachyon.
Type II Strings
Type II String Theory is the easiest String Theory to understand from the RNS Formalism. There are two Type II String Theoryies; The nonchiral Type IIB String Theory,; and the chiral Type IIA String Theory.
Type I Strings
Type I String Theory is the orientifold projection of Type IIB String Theory, but combined with Open String sectors.
Type H Strings
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 DBranes
The Second Superstring Revolution is wellknown for having given rise to DBranes and Dualities between String Theoryies. These discoveries hint towards the existence of a new theory, called MTheory.
Holography, AdS/CFT, and Matrix Theory
A key discovery in the way to nonperturbative 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 AntideSitter 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 nonperturbative formulation of MTheory, but only in AntideSitter 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.
FTheory
FTheory is an interesting formulation of Type IIB String Theory.
Twistor String Theory
Twistor String Theory is String Theory in Twistor Space. It is equivalent to perturbative YangMills Theory.
String Field Theory
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 Formalism
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]}.
MSSM
The MSSM is a Supersymmetric extensionp to the Standard Model. When in the vacua of MTheory, it predicts a Higgs Mass that concurs with experiments ^{[4]}.
String Phenomenology
String Phenomenology refers to finding the predictions of String Theory that can be tested in the real world.
History
Historical Motivation
(1961 to 1968)
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.
Strings
(1969)
When String Theory was initially discovered, it was SMatrix Theory. It was all about SMatrices, Regge Trajectories, and all that; but there was no concept of Strings involved. With the discovery of the NambuGoto Action by Yoichiro Nambu and Tetsou Goto, it became clear that String Theory was a theory of Strings. This was actually a followup 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 Revolution
(19701981)
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 antiperiodic 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 TDuality for Bosonic Strings.
First Superstring Revolution
(19811989)
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 NonOriented 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 Revolution
(19901998)
Joseph Polchinski showed that DBranes were necessary in String Theory.
Edward Witten discovered that the Type IIA String Theory was TDual to the Type IIB String Theory, the Type HE String Theory was TDual to the Type HO String Theory, and that the Type IIB String Theory displayed selfSDuality, whereas the Type I String Theory was SDual to the Type HO String Theory.
Petr Horava and Edward Witten discovered the HoravaWitten String Theory (the SDual 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 MTheory 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 Era
(2000present)
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 MTheory. Since the MSSM predicts a Higgs Mass of 125 GeV/c_{0}^{2}, so do the realistic vacua of MTheory. 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 Tests
Of Supersymmetry
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 MTheory. Since the MSSM predicts a Higgs Mass of 125 GeV/c_{0}^{2}, so do the realistic vacua of MTheory. 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 Dimensions
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.
Applications
In Condensed Matter Physics
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 Theory
AdS/CFT tells us that certain weaklycoupled String Theoryies are equivalyent to certain stronglycoupled Quantum Field Theoryies. This allows us to use Perturbative Techniques\ to study stronglycoupled Quantum Field Theoryies.
References
 ↑ Siegel, W. http://insti.physics.sunysb.edu/~siegel/sft.pdf
 ↑ Siegel, W. http://arxiv.org/pdf/hepth/0107094v1.pdf
 ↑ http://motls.blogspot.in/2005/01/purespinorformalism.html
 ↑ ^{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.
 ↑ Witten, Edward (1996). "FiveBranes and MTheory on an orbifold". Nucl.Phys.B 463 (6): 382397. http://arxiv.org/pdf/hepth/9512219v3.pdf.
 ↑ Sen, Ashok (1996). "Unification of String Dualities". Nucl.Phys.Proc.Suppl. 58 (6): 519. http://arxiv.org/pdf/hepth/9609176.pdf.
 ↑ Townsend, Paul (1996). "Brane Surgery". Nucl.Phys.Proc.Suppl. 58 (6): 163175. http://arxiv.org/pdf/hepth/9512219v3.pdf.
 ↑ Duff, Michael. "The Theory Formerly known as Strings". http://arxiv.org/pdf/hepth/9608117v3.pdf.
 ↑ Banks, Tom; Ficshler, Willy., Shenker, Stephen., Susskind, Leonard. (1996). "M Theory as a Matrix Model: A Conjecture". Physical Review D.```~~~```. 1997 55 (8): 51125228. doi:10.1103/PhysRevD.55.5112. http://arxiv.org/pdf/hepth/9610043v3.pdf.
 ↑ Motl, Lubos; Banks, Thomas. (2001). "Nonperturbative Formulations of Superstring Theory". New Brunswick Rutgers, The State University of New Jersey. http://arxiv.org/pdf/hepth/0109149.pdf.
 ↑ Motl, Lubos; Susskind, Leonard. (1997). "Finite N Heterotic Matrix Models and Discrete Light Cone Quantization". ArXiV. http://arxiv.org/pdf/hepth/9708083v2.pdf.
 ↑ Motl, Lubos; Banks, Thomas. (1997). "Heterotic Strings from Matrices". Journal of High Energy Physics 9712 (4). http://arxiv.org/pdf/hepth/9703218v1.pdf.
 ↑ Motl, Lubos (1997). "Proposals on nonperturbative superstring interactions". ArXiV. http://arxiv.org/pdf/hepth/9701025v3.pdf.
 ↑ Motl, Lubos (1997). "Quaternions and M(atrix) theory in spaces with boundaries". ArXiV. http://arxiv.org/pdf/hepth/9612198v3.pdf.
 ↑ http://motls.blogspot.in/2013/09/cms25sigmaexcessintophiggs.html
 ↑ http://motls.blogspot.in/2013/10/cmssecondbehbosonnear135gevgets.html
 ↑ http://motls.blogspot.in/2013/09/cms3sigmadeficitsinsearchfor.html
 ↑ http://motls.blogspot.com/2013/08/twosigmaishcmsmultileptonexcesses.html
 ↑ Akula, Sujeet.; Nath, Pran., Feldman, Daniel. Peim, Gregory.. "Excess Observed in CDF and SUSY at the LHC". Physics Review D..
 ↑ http://www.lpta.univmontp2.fr/article.php3?id_article=316
 ↑ http://arxiv.org/pdf/astroph/0609189.pdf
 ↑ Hoyle, C. D.; Schmidt, U., Heckel, B.R., Adelberger, E.G., Gundlach, J.H., Kapner, D.J./, Swanson, H.E. (2001). "Submillimeter tests of the gravitational inversesquare law: A search for "large" extra dimensions". Physical Review Letters 86: 14181421. http://arxiv.org/pdf/hepph/0011014v1.pdf.
 ↑ http://motls.blogspot.in/2013/09/cms25sigmaexcessintophiggs.html
 ↑ http://motls.blogspot.in/2013/10/cmssecondbehbosonnear135gevgets.html
 ↑ http://motls.blogspot.in/2013/09/cms3sigmadeficitsinsearchfor.html
 ↑ http://motls.blogspot.com/2013/08/twosigmaishcmsmultileptonexcesses.html
 ↑ Akula, Sujeet.; Nath, Pran., Feldman, Daniel. Peim, Gregory.. "Excess Observed in CDF and SUSY at the LHC". Physics Review D..
 ↑ http://www.lpta.univmontp2.fr/article.php3?id_article=316
 ↑ http://arxiv.org/pdf/astroph/0609189.pdf
 ↑ Hoyle, C. D.; Schmidt, U., Heckel, B.R., Adelberger, E.G., Gundlach, J.H., Kapner, D.J./, Swanson, H.E. (2001). "Submillimeter tests of the gravitational inversesquare law: A search for "large" extra dimensions". Physical Review Letters 86: 14181421. http://arxiv.org/pdf/hepph/0011014v1.pdf.