Notes on R-charged black holes near criticality and gauge theory

After reviewing the thermodynamics and critical phenomena associated with AdS black holes carrying multiple R-charges in various dimensions, we do a Bragg-Williams like analysis of the systems around its critical points. This leads us to propose an effective potential governing the equilibrium properties of the boundary gauge theory. We also study certain non-equilibrium phenomena associated with these gauge theories. In particular, we compute the conductivities and diffusion coefficients for theories with multiple R-charges in four, three and six dimensions.