AdS$_3$ Gravity and RCFT Ensembles with Multiple Invariants

TL;DR

This paper computes gravity partition functions for SU(N) level 1 WZW models with multiple invariants, revealing an ensemble average interpretation consistent with dual CFT descriptions.

Contribution

It introduces a method to explicitly calculate weights for ensemble averages over multiple invariants in AdS$_3$ gravity models.

Findings

Weights are positive for all N, supporting ensemble duality.

Explicit inversion of the matrix of invariants is achieved for arbitrary size.

The approach applies to models with arbitrarily many invariants.

Abstract

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.