Heterotic string theory

The fourth and fifth flavors of superstrings that exist in 10 dimensions are the heterotic string theories.

The heterotic string is a closed string. It is a heterotic or a hybrid of a superstring and a bosonic string. There are two kinds of heterotic superstring theories:

• SO(32)

• E8 x E8

These are often abbreviated as HO or HE. 

Heterotic string theory takes advantage of the notion that, in string theory, left and right moving excitations are completely decoupled. Left moving or counterclockwise excitations are treated as a bosonic string in D=26 dimensions. Right moving or clockwise excitations are treated as a superstring in D=10 dimensions. The difference is the 16 dimensions and they must be compactified on an even, self-dual lattice, of which, there are two possible for 16 dimensions. This is what leads to the two flavors of heterotic string. They differ by the gauge group in 10 dimensions. One is SO(32) and the other is E8 x E8. These are the only two gauge groups that are anomaly-free and can be coupled to the N=1 supergravity in 10 dimensions. 

Heterotic strings must be closed, not open. It is not possible to define any boundary conditions. This is because the left and right moving excitations have a different character. 

Dualities

Heterotic SO(32) superstring is related to the type I superstring theory by S-duality.

Heterotic E8 x E8 and heterotic SO(32) are related to each other by T-duality.