  We study the frequency-dependent conductivity of nodal line semimetals
(NLSMs), focusing on the effects of carrier density and energy dispersion on
the nodal line. We find that the low-frequency conductivity has a rich spectral
structure which can be understood using scaling rules derived from the geometry
of their Dupin cyclide Fermi surfaces. We identify different frequency regimes,
find scaling rules for the optical conductivity in each, and demonstrate them
with numerical calculations of the inter- and intraband contributions to the
optical conductivity using a low-energy model for a generic NLSM.
