The Role of Magnetic Fields in Setting the Star Formation Rate and the
  Initial Mass Function
  Star-forming gas clouds are strongly magnetized, and their ionization
fractions are high enough to place them close to the regime of ideal
magnetohydrodyamics on all but the smallest size scales. In this review we
discuss the effects of magnetic fields on the star formation rate (SFR) in
these clouds, and on the mass spectrum of the fragments that are the outcome of
the star formation process, the stellar initial mass function (IMF). Current
numerical results suggest that magnetic fields by themselves are minor players
in setting either the SFR or the IMF, changing star formation rates and median
stellar masses only by factors of $\sim 2-3$ compared to non-magnetized flows.
However, the indirect effects of magnetic fields, via their interaction with
star formation feedback in the form of jets, photoionization, radiative
heating, and supernovae, could have significantly larger effects. We explore
evidence for this possibility in current simulations, and suggest avenues for
future exploration, both in simulations and observations.
