Abstract
Three-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 different multi-particle sectors in the partition function, which induces an interesting sl(2) structure on the n-particle components of the partition function.
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Mvondo-She, Y., Zoubos, K. On the combinatorics of partition functions in AdS3/LCFT2. J. High Energ. Phys. 2019, 97 (2019). https://doi.org/10.1007/JHEP05(2019)097
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DOI: https://doi.org/10.1007/JHEP05(2019)097