background. In analogy to ’partially massless NMG’ [@Bergshoeff:2009aq; @Grumiller:2010tj] the mass squared of the partially massless mode in an AdS background is negative and saturates the Breitenlohner–Freedman bound [@Breitenlohner:1982bm].

Formally, it is easy to obtain (\[pmaction\]) and (\[infinv\]) in a de Sitter background by replacing $1/\ell^2=-\Lambda$, with positive $\Lambda$. Then (\[pmaction\]) does indeed propagate partially massless modes with positive mass squared.

Because the nature of the additional symmetries at the partially massless point is not clear to us, e.g. whether they exist also at the non-linear level, we will not discuss further the partition function of this particular theory but go on to discuss the better understood critical points of PET gravity and their LCFT duals.

CFT interpretation {#CFTinterpret}
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Following the logic laid out in [@Gaberdiel:2010xv] and [@Bertin:2011jk] we present the partition functions of the conjectured LCFT duals. Lacking a better knowledge/understanding of LCFT partition functions we give only the partition functions corresponding to single-particle log-excitations on the CFT side. We find perfect agreement of the results at that level.\
*Tricritical point* In the double-log case PET gravity is conjectured to be dual to a parity even rank-three LCFT. For such a LCFT the single-particle contribution is $$\label{log2CFT}\hskip 1cm
 