Vacuum alignment and phase structure of holographic bi-layers

We study the D3/probe D5 system with two domain wall hypermultiplets. The conformal symmetry can be broken by a magnetic field, B, (or running coupling) which promotes condensation of the fermions on each individual domain wall. Separation of the domain walls promotes condensation of the fermions between one wall and the other. We study the competition between these two effects showing a first order phase transition when the separation is ~ 0.56 lambda^1/4 B^-1/2. We identify extremal brane configurations which exhibit both condensations simultaneously but they are not the preferred ground state.