Three-dimensional tricritical gravity

We consider a class of parity-even, six-derivative gravity theories in three dimensions. After linearizing around anti-de Sitter space, the theories have one massless and two massive graviton solutions for generic values of the parameters. At a special, so-called tricritical, point in parameter space the two massive graviton solutions become massless, and they are replaced by two solutions with logarithmic and logarithmic-squared boundary behavior. The theory at this point is conjectured to be dual to a rank-3 logarithmic conformal field theory whose boundary stress tensor, central charges, and new anomaly we calculate. We also calculate the conserved Abbott-Deser-Tekin charges. At the tricritical point, these vanish for excitations that obey Brown-Henneaux and logarithmic boundary conditions, while they are generically nonzero for excitations that show logarithmic-squared boundary behavior. This suggests that a truncation of the tricritical gravity theory and its corresponding dual logarithmic conformal field theory can be realized either via boundary conditions on the allowed gravitational excitations, or via restriction to a zero-charge subsector. We comment on the structure of the truncated theory.