My main current research interest is to develop efficient techniques to solve strongly coupled quantum field theories. They have to be applicable to real-world problems (thus: no SUSY, no AdS). Such methods are rare. One example is the conformal bootstrap approach to critical theories in 3 and 2+1 dimensions. A more speculative idea is the Hamiltonian truncation method to study strongly coupled RG flows.
See here if you are looking for a PhD (to start in October 2017).