Gauge invariant response functions in Algebraic Fermi liquids

A new method is developed that permits the simple evaluation of two-loop response functions for fermions coupled to a gauge field. We employ this method to study the gauge-invariant response functions in the Algebraic Fermi liquid, a non-Fermi liquid state proposed to describe the pseudogap phase in the QED3 theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent \eta_4, while other correlators show behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.