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  
This article or section 's content is very similar or exactly the same as that at Wikipedia. This is because the contributor of this article had initially contributed it to wikipedia. 
The RNS Formalism, (naive form known as:RNS String Theory, also known as the RNS SuperString Theory), was an early attempt to introduce fermions through the means of Supersymmetry, into String Theory, which was then only Bosonic String Theory. "RNS" stands for "RamondNeveuSchwarz". It was introduced as a theory with supersymmetry on the Worldsheet, but was later found to be equivalent to the GS String Theory, which has supersymmetry on the background spacetime. In the RNS Formalism, the fields describing the embedding of the Worldsheet in spacetime is actually a bosonic field, and the fermionic fields are spacetime vectors.
(^{[1]}^{[2]}^{[3]}^{[4]})
Action principle
The RNS String Theory is given by the Lagrangian density:' " " ^{[1]}
The corresponding action is given by the RNS Action:
Notice that this is only the Polyakov Action + the Dirac Action. The same action also continues to hold for some GSO truncated string theories, namely the Type IIB String Theory, the Type IIA Theory, and the Type I String Theory.
Sectors
For RNS Open Strings, there are 2 sectors. Namely, the
Ramond sector, with boundary condition:
.
NeveuSchwarz sector, with boundary condition:
.
For RNS closed strings, there are 4 sectors.
First of all, a periodic boundary condition in means that:
.
Whereas an antiperiodic boundary condition in means that:
.
The Ramond Ramond sector is periodic on .
The NeveuSchwarz NeveuSchwarz sector is antiperiodic in .
The Ramond NeveuSchwarz sector is periodic in and antiperiodic in .
The NeveuSchwarz Ramond sector is antiperiodic in and periodic in .
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tag; invalid names, e.g. too many
While in the NeveuSchwarz sector,:^{[2]}^{[3]}^{[4]}
This is clearly a central extension to the SuperWitt algebra. They are expressible in terms of the modes of the oscillations of the string as follows:^{[2]}^{[3]}^{[4]}
Imposing the SuperVirasoro constraints
Imposing SuperVirasoro constraints to get rid of the PauliVillar ghost states, we see that the normal ordering constant must be in the Ramond sector and in the NeveuSchwarz sector. Also, the critical dimension must be . Note, that unlike the Bosonic String Theory, the central charge is no longer equal to the critical dimension, but instead, of it, i.e., in this case, it is .
Unsuitability as a Theory of Everything
Clearly, the mass spectrum, being given by:^{[4]}
In the open string sector, has a tachyon at in the NeveuSchwarz sector (since there, ), . The same logic applies to the NSNS, RNS, NSR, etc. sector of the closed strings, etc.
However, tachyons are unstable due to the Sen Conjecture,^{[4]} also known as Tachyon condensation. The reason being, that that would not allow stable ground states to exist. .
Thus, the naive RNS String Theory cannot be a Theory of Everything, which resulted in the need for the GSO Projection.
Note, however, that this only the naive RNS String Theory. The RNS Formalism, though, can still be used. I.e., the same formalism can be used, but with a GSO Projection, which results in different string theories.
References
 ↑ ^{1.0} ^{1.1} ^{1.2} McMohan, David (2009). String theory DeMystified. Chicago: McGrawHill. ISBN 9780071498708. http://www.nucleares.unam.mx/~alberto/apuntes/mcmahon.pdf.
 ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Michio Kaku (2000). Strings, Conformal Fields, and MTheory. New York: Springer. pp. 3–32. ISBN 9780387988924. http://www.amazon.com/StringsConformalMTheoryGraduateContemporary/dp/0387988920/ref=sr_1_1?s=books&ie=UTF8&qid=1371008020&sr=11&keywords=Strings%2C+Conformal+Fields%2C+and+MTheory.
 ↑ ^{3.0} ^{3.1} ^{3.2} ^{3.3} Mohaupt, Thomas. Introduction to String theory. http://arxiv.org/pdf/hepth/0207249v1.pdf.
 ↑ ^{4.0} ^{4.1} ^{4.2} ^{4.3} ^{4.4} ^{4.5} Szabo, Richard, J.. Introduction to String theory and Dbrane Dynamics. http://arxiv.org/pdf/hepth/0207142v1.pdf.
.