First of all, sorry if this is off-topic

I have decided I want to do a PhD related to causal dynamical triangulations. Unfortunately, there are very few people who are familiar with the subject. Obviously I am going to apply to try to work with these individuals. However, I was wondering if it is possible to apply to work with people who aren't directly familiar with CDT, but instead specialize in relevant topics (e.g. statistical mechanics or some branch of mathematics) and then work on CDT under their supervision. Can a PhD work like this? If so, what types of fields should I be looking into?