Poincaré Series, 3d Gravity and Averages of Rational CFT

Abstract

We investigate the Poincaré approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)${}_k$ WZW models provide unitary examples for which the Poincare series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT's sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU($N$)${}_1$ and SU(3)${}_k$, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions -- the latter corresponding to analogues of 3-manifold "wormholes" -- such that the expected average is correctly reproduced.

arXiv comment52 pages, 8 tables, no chairs

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Cited by in corpus (18)

• Gravity factorized
• Harmonic analysis of 2d CFT partition functions
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• Adding Flavor to the Narain Ensemble
• Chern-Simons Invariants from Ensemble Averages
• Alpha states demystified: Towards microscopic models of AdS${}_2$ holography
• Averaging over moduli in deformed WZW models
• A note on ensemble holography for rational tori
• Microstructure in matrix elements
• AdS${}_3$ Gravity and RCFT Ensembles with Multiple Invariants
• On Classification of Fermionic Rational Conformal Field Theories
• TQFT gravity and ensemble holography
• Gravity without averaging
• Global Symmetries, Code Ensembles, and Sums Over Geometries
• Wormholes and surface defects in rational ensemble holography
• (Half) Wormholes under Irrelevant Deformation
• A universal sum over topologies in 3d gravity
• Factorization and global symmetries in holography