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Effective Field Theory for the Quantum Electrodynamics of a Graphene Wire

We study the low-energy quantum electrodynamics of electrons and holes, in a thin graphene wire. We develop an effective field theory (EFT) based on an expansion in p/p_T, where p_T is the typical momentum of electrons and holes in the transverse direction, while p are the momenta in the longitudinal direction. We show that, to the lowest-order in (p/p_T), our EFT theory is formally equivalent to the exactly solvable Schwinger model. By exploiting such an analogy, we find that the ground state of the quantum wire contains a condensate of electron-hole pairs. The excitation spectrum is saturated by electron-hole collective bound-states, and we calculate the dispersion law of such modes. We also compute the DC conductivity per unit length at zero chemical potential and find g_s =e^2/h, where g_s=4 is the degeneracy factor.