the lines of [@Gaberdiel:2010xv]. We will scan the whole parameter space of PET gravity, covering the critical points found in [@Bergshoeff:2012ev], but also uncovering an additional special point in parameter space: the partially massless limit of linearized six-derivative parity even gravity. Focusing on the critical points we will give further evidence for the conjectured duality of PET gravity to LCFTs of rank two and three.

The AdS/*L*CFT duality only holds for those theories where *all* solutions to the equations of motion are allowed. From the very beginning probably one of the most prominent questions concerning critical gravities was how (and if) one can consistently truncate (some of) the logarithmic solutions by imposing boundary conditions. For example restricting to Brown–Henneaux boundary conditions [@Brown:1986nw] for excitations on the gravity side would kill all log modes. In the prime example of TMG/chiral gravity these are the boundary conditions one has to choose to obtain chiral gravity. If one imposes log boundary conditions [@Grumiller:2008es] one obtains log-TMG which is dual to a LCFT. Recently, using a scalar field toy model, another truncation of critical theories was put forward that allows some, but not all log solutions [@Bergshoeff:2012sc]. In [@Bergshoeff:2012ev] a tricritical version of this 