  We show that the spatial dimensionality of the quantum critical point
associated with Bose--Einstein condensation at T=0 is reduced when the
underlying lattice comprises a set of layers coupled by a frustrating
interaction. For this purpose, we use an heuristic mean field approach that is
complemented and justified by a more rigorous renormalization group analysis.
Due to the presence of an emergent symmetry, i.e. a symmetry of the ground
state that is absent in the underlying Hamiltonian, a three--dimensional
interacting Bose system undergoes a chemical potential tuned quantum phase
transition that is strictly two dimensional. Our theoretical predictions for
the critical temperature as a function of the chemical potential correspond
very well with recent measurements in BaCuSi$_{2}$O$_{6}$.
