  The question of what happens when the heterotic SO(32) instanton becomes
small was answered sometime back by Witten. The heterotic theory develops an
enhanced Sp(2k) gauge symmetry for k small instantons, besides the allowed
SO(32) gauge symmetry. An interesting question now is to ask what happens when
we take the large k limit. In this paper we argue that in some special cases,
where Gauss' law allows the large k limit, the dynamics of the large k small
instantons can be captured by a dual gravitational description. For the cases
that we elaborate in this paper, the gravity duals are non-Kahler manifolds
although in general they could be non-geometric. These small instantons are
heterotic five-branes and the duality allows us to study the strongly coupled
field theories on these five-branes. We review and elaborate on some of the
recent observations pointing towards this duality, and argue that in certain
cases the gauge/gravity duality may be understood as small instanton
transitions under which the instantons smoothen out and consequently lose the
Sp(2k) gauge symmetry. This may explain how branes disappear on the dual side
and are replaced by fluxes. We analyse the torsion classes before and after the
transitions, and discuss briefly how the ADHM sigma model and related vector
bundles could be studied for these scenarios.
