  Motivated by the observation of the fractional quantum Hall effect in
graphene, we consider the effective field theory of relativistic quantum Hall
states. We find that, beside the Chern-Simons term, the effective action also
contains a term of topological nature, which couples the electromagnetic field
with a topologically conserved current of $2+1$ dimensional relativistic fluid.
In contrast to the Chern-Simons term, the new term involves the spacetime
metric in a nontrivial way. We extract the predictions of the effective theory
for linear electromagnetic and gravitational responses. For fractional quantum
Hall states at the zeroth Landau level, additional holomorphic constraints
allow one to express the results in terms of two dimensionless constants of
topological nature.
