I am graduating this semester with a bachelors in physics. My goal is to do theory in my graduate level course work. The problem I am in now is that I missed the deadline to take the physics GRE (I'm taking it in April) so I also missed the deadline to apply to most graduate schools. Fortunately, I was accepted to pursue masters degrees by both the math and physics departments of my current school. My plan is to do one or the other and apply to other schools next semester. My question is which one will be more beneficial to me? Our math department is all around phenomenal... but it won't say "physics" on my applications. Our physics department is good, but it is completely geared towards experimental nuclear physics, which is not my interest (and there is no non-thesis option). Every day now I have been swinging back and forth; math... physics...etc. So, which one would be more beneficial when applying to schools with top theory programs, Math M.S or physics M.S.?
If your MS in physics will be experimental and you want to do theoretical physics, the math route could work. But we are basically guessing at how an admissions committee will see your application; so I encourage you to keep asking. Hopefully other answers here will help.
I'm not a physicist (I'm a philosopher of science who loves mathematical perspectives), so my opinion doesn't count, but here are things to consider.
You may want to think beyond the immediate challenge of getting into a good graduate program.
What possible drawback could there be to a masters in math in your situation? It's not physics, but deeper knowledge and improved ability with math can only help you as a physicist. Surely physics admissions committees will see that. @MartinArgrrami's answer is a good reply to this argument, though. Perhaps certain kinds of experimental physicists will be more impressed by a physics degree with experimental emphasis. On the other hand, deeper experience with math may facilitate additional insights and theoretical opportunities even in experimental research.
The fact that you're even considering a math MS, and the paper you linked, suggest that your orientation to physics will be such that math is not merely one among many tools. If it's the more mathematically inspired corners of physics that you love, then why not work toward that orientation (even if you think you'll exercise your mathematical interests in experimental contexts)?