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

Abstract

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 $E_8 \times E_8$ Heterotic string compactified on $T^2$ is described in M(atrix) theory by N=4 SYM in 3+1 dimensions with base $S^1 \times CP^1$ and a holomorphically varying coupling constant. The $CP^1$ 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 $S^1$ and $T^3$. 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.