GSO Projection

String Theory
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 sector

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 sector

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 Theory

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.