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GSO Projection

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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


The GSO Projection is a projection of states in the RNS Formalism. The GSO Projection maps out the tachyon, thereby ensuring a stable, supersymmetric vacuum and equating the RNS Formalism to the GS Formalism. "GSO" stands for Ferninando Gliozzi, Joel Scherk, and David Olive.

In the Neveu-Schwarz sectorEdit this section

In the Neveu-Schwarz Sector, the GSO Projection is defined as

\mathsf{\mathcal{P}}_{\operatorname{NS}}^{-}\left| \psi  \right\rangle =\left( 1-{{\left( -1 \right)}^{F}} \right)\left| \psi  \right\rangle

In the Ramond sectorEdit this section

In the Ramond sector, the GSO Projection could be either defined as:

    \mathsf{\mathcal{P}}_{\operatorname{R}}^{-}\left| {{\psi }} \right\rangle =\left( 1-\left( \prod\limits_{k=1}^{10}{{{\gamma }_{k}}} \right){{\left( -1 \right)}^{F}} \right)\left| {{\psi }} \right\rangle

or as

   \mathsf{\mathcal{P}}_{\operatorname{R}}^{+}\left| {{\psi }} \right\rangle =\left( 1+\left( \prod\limits_{k=1}^{10}{{{\gamma }_{k}}} \right){{\left( -1 \right)}^{F}} \right)\left| {{\psi }} \right\rangle

Type II String TheoryEdit this section

GSO Projecting the naive RNS String Theory immediately results in the Type IIB String Theory and Type IIA String Theory. The Type IIB String Theory is non-chiral, whereas the Type IIA String Theory is chiral.

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