I am not sure that "hot topic" is an advisable criterion for a Ph.D. research project, since this will typically mean that easy/doable questions have been done and only the hard/intractable questions remain. You might want to base your choice on a department that offers a broad range of topics in mathematical physics, including QFT. The offer of <A HREF="https://www.york.ac.uk/maths/research/mathematical-physics-quantum-information/phd/">York University</A> seems attractive, just by way of example.