Poincaré series, 3d gravity and averages of rational CFT

• Main Authors: Viraj Meruliya, Sunil Mukhi, Palash Singh
• Format: Article
• Language: English
• Published: SpringerOpen 2021-04-01
• Series: Journal of High Energy Physics
• Subjects: AdS-CFT Correspondence; Conformal Field Theory; Field Theories in Lower Dimensions; Models of Quantum Gravity
• Online Access: https://doi.org/10.1007/JHEP04(2021)267

Abstract We investigate the Poincaré series 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 Poincaré 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.