  Incompressible even denominator fractional quantum Hall states at fillings
$\nu = \pm \frac{1}{2}$ and $\nu = \pm \frac{1}{4}$ have been recently observed
in monolayer graphene. We use a Chern-Simons description of multi-component
fractional quantum Hall states in graphene to investigate the properties of
these states and suggest variational wavefunctions that may describe them. We
find that the experimentally observed even denominator fractions and standard
odd fractions (such as $\nu=1/3, 2/5$, etc.) can be accommodated within the
same flux attachment scheme and argue that they may arise from sublattice or
chiral symmetry breaking orders (such as charge-density-wave and
antiferromagnetism) of composite Dirac fermions, a phenomenon unifying integer
and fractional quantum Hall physics for relativistic fermions. We also discuss
possible experimental probes that can narrow down the candidate broken symmetry
phases for the fractional quantum Hall states in the zeroth Landau level of
monolayer graphene.
