The GSO projection is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the worldsheet

Worldsheet

In string theory, a worldsheet is a two-dimensional manifold which describes the embedding of a string in spacetime. The term was coined by Leonard Susskind around 1967 as a direct generalization of the world line concept for a point particle in special and general relativity.The type of string,...

 conformal field theory

Conformal field theory

A conformal field theory is a quantum field theory that is invariant under conformal transformations...

 (CFT)--usually those with specific worldsheet fermion

Fermion

In particle physics, a fermion is any particle which obeys the Fermi–Dirac statistics . Fermions contrast with bosons which obey Bose–Einstein statistics....

 number and periodicity

Periodic function

In mathematics, a periodic function is a function that repeats its values in regular intervals or periods. The most important examples are the trigonometric functions, which repeat over intervals of length 2π radians. Periodic functions are used throughout science to describe oscillations,...

 conditions. Such a projection is necessary to obtain a consistent worldsheet CFT. For the projection to be consistent, the set A of operators retained by the projection must satisfy:

• Closure - The operator product expansion
  Operator product expansion
  - 2D Euclidean quantum field theory :In quantum field theory, the operator product expansion is a Laurent series expansion of two operators...
  
   (OPE) of any two operators in A contains only operators which are in A.
• Mutual locality - There are no branch cuts in the OPE of any two operators in the set A.
• Modular invariance - The partition function on the two-torus of the theory containing only the operators in A respects modular invariance
  Modular invariance
  In theoretical physics, modular invariance is the invariance under the group such as SL of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory....
  
  .

Starting from the same worldsheet CFT, different choices in the GSO projection will lead to string theories with different physical particles and properties in spacetime

Spacetime

In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

. For example, the Type II

Type II string theory

In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings. These account for two of the five consistent superstring theories in ten dimensions. Both theories have the maximal amount of supersymmetry — namely 32 supercharges...

 and Type 0

Type 0 string theory

The Type 0 string theory is a less well-known model of string theory. It is a superstring theory in the sense that the worldsheet theory is supersymmetric. However, the spacetime spectrum is not supersymmetric and, in fact, does not contain any fermions at all. In dimensions greater than two, the...

 string theories result from different GSO projections on the same worldsheet theory. Furthermore, the two distinct Type II theories, IIA and IIB, differ in their GSO projections. In building models of realistic string vacua (as opposed to toy model

Toy model

In physics, a toy model is a simplified set of objects and equations relating them that can nevertheless be used to understand a mechanism that is also useful in the full, non-simplified theory....

s), one typically chooses a GSO projection which eliminates the tachyon

Tachyon

A tachyon is a hypothetical subatomic particle that always moves faster than light. In the language of special relativity, a tachyon would be a particle with space-like four-momentum and imaginary proper time. A tachyon would be constrained to the space-like portion of the energy-momentum graph...

ic ground state of the string and preserves spacetime supersymmetry

Supersymmetry

In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...

.