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Poincaré series, 3d gravity and averages of rational CFT
Ist Teil von
The journal of high energy physics, 2021-04, Vol.2021 (4), p.1-49, Article 267
Ort / Verlag
Berlin/Heidelberg: Springer Berlin Heidelberg
Erscheinungsjahr
2021
Link zum Volltext
Quelle
EZB Electronic Journals Library
Beschreibungen/Notizen
A
bstract
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.