  Coulomb interaction might have important effects on the physical observables
in topological semimetals with vanishing density of states at the band touching
due to the weak screening. In this work, we show that Kohn's theorem is not
fulfilled in nodal-line semimetals (NLSMs), which implies non-vanishing
interaction corrections to the conductivity. Using renormalized perturbation
theory, we determine the first-order optical conductivity in a clean NLSM to be
$\sigma_{\perp \perp}(\Omega) = 2 \sigma_{\parallel \parallel}(\Omega) =
\sigma_0 [1 + C_2 \alpha_R(\Omega)]$, where $\perp$ and $\parallel$ denote the
perpendicular and parallel components with respect to the nodal loop, $\sigma_0
= (2 \pi k_0) e^2/(16h)$ is the conductivity in the noninteracting limit, $2
\pi k_0$ is the nodal loop perimeter, $C_2 = (19-6\pi)/12 \simeq 0.013$ is a
numerical constant and $\alpha_R(\Omega)$ is the renormalized fine structure
constant in the NLSM. The analogies between NLSMs and 2D Dirac fermions are
reflected in the universal character of the correction $C_2 \alpha_R(\Omega)$,
which is exactly parallel to that of graphene. Finally, we analyze some
experiments that have determined the optical conductivity in NLSMs, discussing
the possibility of experimentally measuring our result.
