subgroup of the non-compact group $Sp(28)$. (Later, in other contexts, the symbol $Sp(n)$ will represent a compact group.) The analog of the Narain moduli space in this case is $${\cal M}  = E_7(\ZZ)\backslash E_{7,7}/SU(8).$$ The scalar fields of $N=8$ supergravity parametrize this 70-dimensional space. As in the $N=4$ heterotic theory, there are once again 28 $U(1)$ gauge fields. However, this time only 12 of their electric charges are excited (by Kaluza–Klein and winding excitations) in the perturbative string spectrum. The remaining 16 electric charges and all of the magnetic charges are only carried by non-perturbative excitations. One way of understanding this is to note the decomposition $$E_7(\ZZ) \supset SO(6,6;\ZZ) \times SL(2,\ZZ),$$ which exhibits the $T$ duality and $S$ duality subgroups. With respect to this subgroup, the fundamental [**56**]{} representation decomposes as ${\bf 56} = ({\bf 12}, {\bf 2})
+ ({\bf 32}, {\bf 1} )$. The 12 electric charges that occur perturbatively are carried by states whose mass is finite at weak coupling in the string metric. They are associated to the first term, as are the dual magnetic charges, which give states whose mass is proportional to $1/\lambda^2$. The 16 electric and magnetic charges associated to the 32-dimensional spinorial representation 