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

We use AdS/CFT 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 AdS description. For μ = 0, there is a known first order phase transition around a critical temperature Tc. We find that the Higgs VEV is a suitable order parameter for this transition; for T > Tc, the theory is driven to a non-trivial point on the Higgs branch. For μ 6= 0 and T = 0, the Higgs potential is unbounded from below, leading to an instability of the field theory due to Bose-Einstein condensation. [email protected], [email protected], [email protected], [email protected]