**Authors:**
Alessandro Giuliani, Vieri Mastropietro, Marcello Porta

**Title:** *
A lattice gauge theory model for graphene:
critical exponents and anomalous gap
*

**Abstract: **
The effects of the electromagnetic (e.m.) electron-electron
interaction in half-filled graphene are investigated
in terms of a lattice gauge theory model where tight binding
electrons hopping on a honeycomb lattice are coupled to a
three-dimensional quantum e.m. field. By using exact
Renormalization Group methods and lattice Ward Identities, we show that the
quasi-particle weight vanishes at the Fermi points and the effective Fermi
velocity tends to the speed of light as power laws with non-universal
critical exponents. The analysis of the response functions indicates a
tendency towards excitonic pairing. By a variational argument on
the ground state energy, we derive exact non-BCS self-consistence equations for
the excitonic gap, admitting a non-trivial solution if its critical
exponent exceeds a critical value.

**Keywords:**
Graphene, Dirac fermions, Coulomb interactions, Ward identities,
Renormalization Group, lattice gauge theory

Alessandro Giuliani

Dipartimento di Matematica

Università di Roma Tre

L.go S. Leonardo Murialdo 1, 00146 Roma - Italy

e-mail: giuliani AT mat DOT uniroma3 DOT it

Vieri Mastropietro

Dipartimento di Matematica

Università di Roma Tor Vergata

V.le della Ricerca Scientifica 1, 00133 Roma - Italy

e-mail: mastropi AT mat DOT uniroma2 DOT it

Marcello Porta

Dipartimento di Fisica

Università di Roma Sapienza

P.le A. Moro, 00185 Roma - Italy

e-mail: marcello DOT porta AT roma1 DOT infn DOT it