Global aspects of Scherk-Schwarz dimensional reduction are discussed and it
is shown that it can usually be viewed as arising from a compactification on
the compact space obtained by identifying a (possibly non-compact) group
manifold G under a discrete subgroup Gamma, followed by a truncation. This
allows a generalisation of Scherk-Schwarz reductions to string theory or
M-theory as compactifications on G/Gamma, but only in those cases in which
there is a suitable discrete subgroup of G. We analyse such compactifications
with flux and investigate the gauge symmetry and its spontaneous breaking. We
discuss the covariance under O(d,d), where d is the dimension of the group G,
and the relation to reductions with duality twists. The compactified theories
promote a subgroup of the O(d,d) that would arise from a toroidal reduction to
a gauge symmetry, and we discuss the interplay between the gauge symmetry and
the O(d,d,Z) T-duality group, suggesting the role that T-duality should play in
such compactifications.Comment: 43 page
