Heterotic M(atrix) theory at generic points in Narain moduli space

Type II compactifications with varying string coupling can be described elegantly in F-theory/M-theory as compactifications on U-manifolds. Using a similar approach to describe super Yang-Mills with a varying coupling constant, we argue that at generic points in Narain moduli space, the E8 x E8 heterotic string compactified on T2 is described in M(atrix) theory by N=4 SYM in 3+1 dimensions with base S1 x CP1 and a holomorphically varying coupling constant. The CP1 is best described as the base of an elliptic K3 whose fibre is the complexified coupling constant of the super Yang-Mills theory leading to manifest U-duality. We also consider the cases of the heterotic string on S1 and T3. The twisted sector seems to (almost) naturally appear at precisely those points where enhancement of gauge symmetry is expected and need not be postulated. A unifying picture emerges in which the U-manifolds which describe type II orientifolds (dual to the heterotic string) as M- or F-theory compactifications play a crucial role in heterotic M(atrix) theory compactifications. (orig.)