scalar field toy model was generalized to interacting spin-two fields. Calculations on the linearized level seemed to lend support to the possibility of truncating the theory. However, it was shown that the theory is flawed with a linearization instability [@Apolo:2012he] and only makes sense either as dual to a LCFT by allowing all solutions, or, imposing Brown–Henneaux boundary conditions, as a ’trivial’ theory propagating null modes.

In the second part of this work we introduce an idea on how such a truncation via boundary conditions could be understood at the level of the partition function. To do so we will interpret the partition function as a sum over quasi-normal mode frequencies following the idea of [@Denef:2009kn]. The authors of [@Denef:2009kn] emphasize that translating from the heat-kernel to the quasi-normal mode spectrum would allow one to pick out the contribution of only one mode or only one frequency to the partition function. We try to turn this argument around by using it to dismiss the contributions of certain modes. Our “truncation” will effectively be a prescription on which quasi-normal modes to keep in the spectrum and which not to keep. We obtain results concurrent with the comment made in the previous 