  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.
