Strong coupling effective Higgs potential and a first order thermal phase transition from AdS/CFT duality

We use anti--de Sitter/conformal field theory duality to study the thermodynamics of a strongly coupled N=2 supersymmetric large Nc SU(Nc) gauge theory with Nf=2 fundamental hypermultiplets. At finite temperature T and isospin chemical potential μ, a potential on the Higgs branch is generated, corresponding to a potential on the moduli space of instantons in the anti--de Sitter description. For μ=0, there is a known first order phase transition around a critical temperature Tc. We find that the Higgs vacuum expectation value is a suitable order parameter for this transition; for T>Tc, the theory is driven to a nontrivial point on the Higgs branch. For μ≠0 and $T=0$, the Higgs potential is unbounded from below, leading to an instability of the field theory due to Bose-Einstein condensation.