AdS$_3$ Gravity and RCFT Ensembles with Multiple Invariants

Understand

We use the Poincar\'e series method to compute gravity partition functions associated to SU(N) level 1 WZW models with arbitrarily large numbers of modular invariants.

• The result is an average over these invariants, with the weights being given by inverting a matrix whose size is of order the number of invariants.
• For the chosen models, this matrix takes a special form that allows us to invert it for arbitrary size and thereby explicitly calculate the weights of this average.
• For the identity seed we find that the weights are positive for all N, consistent with each model being dual to an ensemble average over CFT's.