AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants

Abstract

We use the Poincaré 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.

arXiv comment17 pages, 1 table; typos corrected, references added

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• Wormholes and surface defects in rational ensemble holography
• (Half) Wormholes under Irrelevant Deformation
• Factorization and global symmetries in holography
• A universal sum over topologies in 3d gravity