Vertex Corrections in Gauge Theories for Two-dimensional Condensed Matter Systems

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1/q , 1 < η ≤ 2, the fermionic self-energy without vertex corrections vanishes for small frequencies ω as Σ(ω) ∝ ω with γ = 2 1+η < 1. We show that inclusion of the leading radiative correction to the fermion gauge field vertex leads to Σ(ω) ∝ ω [1 − aη ln(ω0/ω)], where aη is a positive numerical constant and ω0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent γ to larger values.