Heterotic string theory


In string theory, a heterotic string is a closed string which is a hybrid of a superstring and a bosonic string. There are two kinds of heterotic string, the heterotic SO and the heterotic E8 × E8, abbreviated to HO and HE. Heterotic string theory was first developed in 1985 by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm, in one of the key papers that fueled the first superstring revolution.

Overview

In string theory, the left-moving and the right-moving excitations are completely decoupled, and it is possible to construct a string theory whose left-moving excitations are treated as a bosonic string propagating in D = 26 dimensions, while the right-moving excitations are treated as a superstring in D = 10 dimensions.
The mismatched 16 dimensions must be compactified on an even, self-dual lattice. There are two possible even self-dual lattices in 16 dimensions, and it leads to two types of the heterotic string. They differ by the gauge group in 10 dimensions. One gauge group is SO while the other is E8 × E8.
These two gauge groups also turned out to be the only two anomaly-free gauge groups that can be coupled to the N = 1 supergravity in 10 dimensions. 496 and E8 × U
Every heterotic string must be a closed string, not an open string; it is not possible to define any boundary conditions that would relate the left-moving and the right-moving excitations because they have a different character.

String duality

is a class of symmetries in physics that link different string theories. In the 1990s, it was realized that the strong coupling limit of the HO theory is type I string theory — a theory that also contains open strings; this relation is called S-duality. The HO and HE theories are also related by T-duality.
Because the various superstring theories were shown to be related by dualities, it was proposed that each type of string was a different limit of a single underlying theory called M-theory.