I need some help deciding what to do in grad school. My ultimate goal is to do research in purely theoretical physics, probably in LQG, or perhaps in String theory, or something of this nature (spare me the talk about never getting a job - I know). I'd like to do this from a very formal and mathematical point of view. I'm about to graduate with a double major in Physics and Mathematics, and need to decide what to do for grad school. My current plan is to do a Masters in math, on Lie groups, specifically related to physics, and then go do a PhD in physics, in LQG or whatever specific field I'll have decided on by then. Does this make sense? Do Lie groups play an important enough role that getting a Masters in it will actually help? Would a masters in another area of mathematics be more useful?