Mvondo-She, YannickZoubos, Konstantinos2021-02-042021-02-042019-05-17Mvondo-She, Y., Zoubos, K. On the combinatorics of partition functions in AdS3/LCFT2. Journal of High Energy Physics 2019, 97 (2019). https://doi.org/10.1007/JHEP05(2019)097.1029-8479 (online)10.1007/JHEP05(2019)097http://hdl.handle.net/2263/78244Three-dimensional Topologically Massive Gravity at its critical point has been conjectured to be holographically dual to a Logarithmic CFT. However, many details of this correspondence are still lacking. In this work, we study the 1-loop partition function of Critical Cosmological Topologically Massive Gravity, previously derived by Gaberdiel, Grumiller and Vassilevich, and show that it can be usefully rewritten as a Bell polynomial expansion. We also show that there is a relationship between this Bell polynomial expansion and the plethystic exponential. Our reformulation allows us to match the TMG partition function to states on the CFT side, including the multi-particle states of t (the logarithmic partner of the CFT stress tensor) which had previously been elusive. We also discuss the appearance of a ladder action between the di erent multi-particle sectors in the partition function, which induces an interesting sl(2) structure on the n-particle components of the partition function.en© The Authors. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0).AdS-CFT correspondenceClassical theories of gravityConformal and W symmetryConformal field models in string theoryArticle