These lead to two version of the heterotic string known as the E 8 & times; E 8 heterotic string and the SO ( 32 ) heterotic string.
22.
The heterotic superstrings come in two types SO ( 32 ) and E 8 & times; E 8 as indicated above and the type I superstrings include open strings.
23.
Heterotic M-theory has been used to construct models of brane cosmology in which the observable universe is thought to exist on a brane in a higher dimensional ambient space.
24.
Witten's proposal was based on the observation that type IIA and E 8 �E 8 heterotic string theories are closely related to a gravitational theory called eleven-dimensional supergravity.
25.
For example, a subclass of the K3 manifolds is elliptically fibered, and F-theory on a K3 manifold is dual to heterotic string theory on a two-torus.
26.
In the 1980s Donagi applied algebraic geometry to string theory and related theories such as supersymmetric Yang-Mills theories in order to develop models for heterotic string theory from suitable compactifications.
27.
Prior to 1995, theorists believed that there were five consistent versions of superstring theory ( type I, type IIA, type IIB, and two versions of heterotic string theory ).
28.
For example, type IIA string theory is equivalent to type IIB string theory via T-duality, and the two versions of heterotic string theory are also related by T-duality.
29.
One way to incorporate the standard model of particle physics into heterotic string theory is the symmetry breaking of E 8 to its maximal subalgebra SU ( 3 ) & times; E 6.
30.
This is because a quadratic term is present in the low energy effective action of heterotic string theory, and it also appears in six-dimensional Calabi Yau compactifications of M-theory.
