  The formation of intra-layer and inter-layer exciton condensates in a model
of a double monolayer Weyl semi-metal is studied in the strong coupling limit
using AdS/CFT duality. We find a rich phase diagram which includes phase
transitions between inter-layer and intra-layer condensates as the charge
densities and the separation of the layers are varied. The tendency to
inter-layer condensation is strongest when the charge densities are balanced so
that the weak coupling electron and hole Fermi surfaces would be nested. For
systems with multiple species of massless Fermions, we find a novel phase
transition where the charge balance for nesting occurs spontaneously.
