I will discuss conditions that must be imposed on conformal field theories at large N in order to reproduce the universal phase structure of Einstein gravity. I will first review the 2d case and discuss the sparseness condition introduced by Hartman, Keller and Stoica. Then, I will proceed to the generalisation to arbitrary dimensions. I will also introduce orbifold CFTs for $d>2$ as an example of a vast landscape of CFTs and show that unlike in two dimensions, they don't universally reproduce the thermal phase structure of gravity.