In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). In string theory, the left-moving and the right-moving excitations almost do not talk to each other, and it is possible to construct a string theory whose left-moving (counter-clockwise) excitations "think" that they live on a bosonic string propagating in D = 26 dimensions, while the right-moving (clock-wise) excitations "think" that they belong to 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.
Heterotic string theory was discovered in 1985 by David Gross, Jeffrey Harvey, Emil Martinec, and Ryan Rohm, in one of the key papers that fueled the first superstring revolution. 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. On the other hand, the strongly coupled limit of the HE theory is M-theory compactified on a line interval (bounded by Horava-Witten domain walls, as explained by Petr Horava and Edward Witten).
Every heterotic string must be a closed string, not an open string, because 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!