  The effects of the electromagnetic (e.m.) electron-electron interactions in
half-filled graphene are investigated in terms of a lattice gauge theory model.
By using exact Renormalization Group methods and lattice Ward Identities, we
show that the e.m. interactions amplify the responses to the excitonic pairings
associated to a Kekul\'e distortion and to a charge density wave. The effect of
the electronic repulsion on the Peierls-Kekul\'e instability, usually
neglected, is evaluated by deriving an exact non-BCS gap equation, from which
we find evidence that strong e.m. interactions among electrons facilitate the
spontaneous distortion of the lattice and the opening of a gap.
