Large N effects on thermal phase transition

We compute leading order corrections to different thermodynamic quantities due to higher derivative couplings effects, and examine the possibilities of large $N$ Hawking-Page thermal phase transitions as finite temperature effect in the (super) Yang-Mills gauge theory and its anti-de Sitter dual. The large $N$ theory defined with $k=+1$ and Anti-de Sitter space as a reference background has a low temperature phase with a free energy $F=0$ - a confining phase - and a high temperature phase with a free energy $F<0$ (i.e. $F\propto N^2$) - an unconfining phase. For $k=-1$ theory, for which the extremal state is taken as a reference background, there is no thermal phase transition in the large $N$ limit.