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 N-c SU(N-c) gauge theory with N-f=2 fundamental hypermultiplets. At finite temperature T and isospin chemical potential mu, 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 mu=0, there is a known first order phase transition around a critical temperature T-c. We find that the Higgs vacuum expectation value is a suitable order parameter for this transition; for T > T-c, the theory is driven to a nontrivial point on the Higgs branch. For mu not equal 0 and T=0, the Higgs potential is unbounded from below, leading to an instability of the field theory due to Bose-Einstein condensation.