Gauge-invariant response functions in algebraic Fermi liquids

A method is developed that permits a 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 ${\mathrm{QED}}_3$ theory of cuprate superconductors. The staggered spin susceptibility is found to exhibit a characteristic anomalous dimension exponent ${\eta }_4,$ while other correlators show a behavior consistent with the conservation laws imposed by the symmetries of the underlying theory.