  We investigate the interrelation between topology and Narain T-duality of
heterotic flux vacua. We present evidence that all 5 and 4-dimensional
Minkowski space heterotic flux backgrounds with 8 supercharges have a locus in
the moduli space with a T-dual description in terms of a compactification on
the product of a K3 surface with a circle or a torus. A test of this
equivalence is provided by calculating the new supersymmetric index on both
sides of the duality. We examine the implications of these dualities for
CHL-like orbifolds that reduce the rank of the gauge group, as well as those
that lead to minimal supersymmetry in 4 dimensions. We also discuss properties
of flux vacua that preserve minimal supersymmetry in 4 dimensions that cannot
be related to conventional compactifications by Narain T-duality. Along the way
we point out a number of properties of these vacua, including the role played
by non-trivial flat gerbes, the appearance of rational worldsheet CFTs in
decompactification limits, and the role of attractive K3 surfaces in
backgrounds with minimal supersymmetry. Finally, we discuss the dual pairs from
the perspective of M-theory/heterotic duality.
