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If I don't make it into medical school, I am thinking about what field I should continue to study. The field of physics that I actually like is mathematical physics, including gauge field theories in non-abelian algebras and string theory, I would prefer to have a job in academia, so my question is should I pursue a PhD in Mathematics in Algebra or Algebraic Geometry, and do research in string theory, or go for a PhD in theoretical physics, (but this will probably require me to find work in non-academic setting.)

If the answer to both is that it is hard to get a job in academia, then I will probably just try to get a PhD in computer sciences in numerical analysis and look for an industrial job, but then my question is: when I am in this setting, if I have contacts with old physics professors, is it practical for me to expect to be able to publish research (the work will be done in my spare time)?