  The observed 97.7% optical transparency of graphene has been linked to the
value 1/137 of the fine structure constant, by using results for noninteracting
Dirac fermions. The agreement in three significant figures requires an
explanation for the apparent unimportance of the Coulomb interaction. Using
arguments based on Ward identities, the leading corrections to the optical
conductivity due to the Coulomb interactions are correctly computed (resolving
a subtle theoretical issue) and shown to amount to only 1-2%, corresponding to
0.03-0.04% in the transparency.
