Heterotic string theory

Overview

In string theory, the left-moving and the right-moving excitations of strings are completely decoupled for a closed string, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations are treated as a bosonic string propagating in D = 26 dimensions, while the right-moving (clockwise) excitations are treated as a superstring in D = 10 dimensions.

The mismatched 16 dimensions must be compactified on an even, self-dual lattice (a discrete subgroup of a linear space). 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(32) (the HO string) while the other is E₈ × E₈ (the HE string).

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. (Although not realized for quite some time, U(1)⁴⁹⁶ and E₈ × U(1)²⁴⁸ are anomalous.)

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.