is a circle $S^1$, whereas in the $E_8 \times
E_8$ case it is a line interval $I$, or (more precisely) an $S^1/\ZZ_2$ orbifold. This means that in the $E_8 \times E_8$ case one can visualize the space-time as an 11d space-time with two 10d faces, which are sometimes referred to as “end-of-the-world 9-branes,” since they have nine spatial dimensions.[@horava95] One of the $E_8$ gauge groups is associated to each face. In any case, at strong coupling the faces move apart and (away from the faces) the theory is described by the same 11d bulk theory that describes the IIA theory at strong coupling. This 11d theory is described in leading order in a low-energy expansion by 11d supergravity, a classical field theory that was discovered almost 20 years ago.[@cremmer78c] It is not yet known what is the correct algorithm that determines all the higher-dimension terms of the low-energy expansion of the effective action, but since we are confident that there is a consistent quantum theory, such an algorithm should exist. The unknown 11d quantum theory is referred to as M theory. As we will discuss, certain of its supersymmetric solitons are known, and they provide a handle on many of 