Three-dimensional AdS gravity and extremal CFTs at c = 8m

We note that Witten's proposed duality between extremal c = 24k CFTs and three-dimensional anti-de Sitter gravity may possibly be extended to central charges that are multiples of 8, for which extremal self-dual CFTs are known to exist up to c = 40. All CFTs of this type with central charges c≥24, provided that they exist, have the required mass gap and may serve as candidate duals to three-dimensional gravity at the corresponding values of the cosmological constant. Here, we compute the genus one partition function of these theories up to c = 88, we give exact and approximate formulas for the degeneracies of states, and we determine the genus two partition functions of the theories up to c = 40