  We study matter with central charge $c >1$ coupled to two-dimensional (2d)
quantum gravity, here represented as causal dynamical triangulations (CDT). 2d
CDT is known to provide a regularization of (Euclidean) 2d Ho\v{r}ava-Lifshitz
quantum gravity. The matter fields are massive Gaussian fields, where the mass
is used to monitor the central charge $c$. Decreasing the mass we observe a
higher order phase transition between an effective $c=0$ theory and a theory
where $c>1$. In this sense the situation is somewhat similar to that observed
for "standard" dynamical triangulations (DT) which provide a regularization of
2d quantum Liouville gravity. However, the geometric phase observed for $c >1$
in CDT is very different from the corresponding phase observed for DT.
