String Theory: Five Theories
In the wake of 1984’s superstring revolution, work on string theory reached a fever pitch. If anything, it proved a little too successful. It turned out that instead of one superstring theory to explain the universe, there were five, summarized here.
And, once again, each one almost matched our world . . . but not quite. By the time the decade ended, physicists had developed and dismissed many variants of string theory in the hopes of finding the one true formulation of the theory.
Instead of one formulation, though, five distinct versions of string theory proved to be selfconsistent. Each had some properties that made physicists think it would reflect the physical reality of our world — and some properties that are clearly not true in our universe.
The distinctions between these theories are mathematically sophisticated. Here are their names and basic definitions, which are important mainly because of the key role they play in Mtheory.

Type I string theory: Type I string theory involves both open and closed strings. It contains a form of symmetry that’s mathematically designated as a symmetry group called O(32).

Type IIA string theory: Type IIA string theory involves closed strings where the vibrational patterns are symmetrical, regardless of whether they travel left or right along the closed string. Type IIA open strings are attached to structures called Dbranes with an odd number of dimensions.

Type IIB string theory: Type IIB string theory involves closed strings where the vibrational patterns are asymmetrical, depending upon whether they travel left or right along the closed string. Type IIB open strings are attached to Dbranes (discovered in 1995) with an even number of dimensions.
A new form of string theory, called heterotic string theory, was discovered in 1985 by the Princeton team of David Gross, Jeff Harvey, Emil Martinec, and Ryan Rohm. This version of string theory sometimes acted like bosonic string theory and sometimes acted like superstring theory.
A distinction of the heterotic string is that the string vibrations in different directions resulted in different behaviors. “Leftmoving” vibrations resembled the old bosonic string, while “rightmoving” vibrations resembled the Type II strings. The heterotic string seemed to contain exactly the properties that Green and Schwarz needed to cancel out anomalies within the theory.
It was ultimately shown that only two mathematical symmetry groups could be applied to heterotic string theory, which resulted in stable theories in ten dimensions — O(32) symmetry and E_{8} x E_{8} symmetry. These two groups gave rise to the names Type HO and Type HE string theory.

Type HO string theory: Type HO is a form of heterotic string theory. The name comes from the longer name Heterotic O(32) string theory, which describes the symmetry group of the theory. It contains only closed strings whose rightmoving vibrations resemble the Type II strings and whose leftmoving vibrations resemble the bosonic strings. The similar theory, Type HE, has subtle but important mathematical differences regarding the symmetry group.

Type HE string theory: Type HE is another form of heterotic string theory, based on a different symmetry group from the Type HO theory. The name comes from the longer name Heterotic E_{8} x E_{8} string theory, based on the symmetry group of the theory. It also contains only closed strings whose rightmoving vibrations resemble the Type II strings and whose leftmoving vibrations resemble the bosonic strings.