|All Roads Lead to String Theory (Polchinski)|
Prior to the First Superstring Revolution
|Early History|| S-Matrix Theory|
|Bosonic String Theory|| Worldsheet|
Bosonic String Theory
String Perturbation Theory
|Supersymmetric Revolution|| Supersymmetry|
|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|
Horava-Witten String Theory
N=4 Super-Yang-Mills Theory
BFSS Matrix Theory
Matrix String Theory
Twistor String Theory
String Field Theory
Pure Spinor Formalism
After the Revolutions
|Phenomenology|| String Theory Landscape|
Minimal Supersymmetric Standard Model
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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 "Ramond-Neveu-Schwarz". 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.
Action principleEdit this section
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.
SectorsEdit this section
For RNS Open Strings, there are 2 sectors. Namely, the
Ramond sector, with boundary condition:
Neveu-Schwarz 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 Neveu-Schwarz Neveu-Schwarz sector is antiperiodic in .
The Ramond Neveu-Schwarz sector is periodic in and antiperiodic in .
The Neveu-Schwarz Ramond sector is antiperiodic in and periodic in .
Imposing the Super-Virasoro constraintsEdit this section
Imposing Super-Virasoro constraints to get rid of the Pauli-Villar ghost states, we see that the normal ordering constant must be in the Ramond sector and in the Neveu-Schwarz 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 EverythingEdit this section
Clearly, the mass spectrum, being given by:
In the open string sector, has a tachyon at in the Neveu-Schwarz sector (since there, ), . The same logic applies to the NS-NS, R-NS, NS-R, etc. sector of the closed strings, etc.
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.
ReferencesEdit this section
- ↑ 1.0 1.1 1.2 McMohan, David (2009). String theory DeMystified. Chicago: McGrawHill. ISBN 978-0071498708. http://www.nucleares.unam.mx/~alberto/apuntes/mcmahon.pdf.
- ↑ 2.0 2.1 2.2 2.3 Michio Kaku (2000). Strings, Conformal Fields, and M-Theory. New York: Springer. pp. 3–32. ISBN 978-0387988924. http://www.amazon.com/Strings-Conformal-M-Theory-Graduate-Contemporary/dp/0387988920/ref=sr_1_1?s=books&ie=UTF8&qid=1371008020&sr=1-1&keywords=Strings%2C+Conformal+Fields%2C+and+M-Theory.
- ↑ 3.0 3.1 3.2 3.3 Mohaupt, Thomas. Introduction to String theory. http://arxiv.org/pdf/hep-th/0207249v1.pdf.
- ↑ 4.0 4.1 4.2 4.3 4.4 4.5 Szabo, Richard, J.. Introduction to String theory and D-brane Dynamics. http://arxiv.org/pdf/hep-th/0207142v1.pdf.
- ↑ Michio Kaku (2000). Strings, Conformal Fields, and M-Theory. New York: Springer. pp. 3–32. ISBN 978-0387988924. http://www.amazon.com/Strings-Conformal-M-Theory-Graduate-Contemporary/dp/0387988920/ref=sr_1_1?s=books&ie=UTF8&qid=1371008020&sr=1-1&keywords=Strings%2C+Conformal+Fields%2C+and+M-Theory.