  We consider the optical conductivity of a clean two-dimensional metal near a
quantum spin-density-wave transition. Critical magnetic fluctuations are known
to destroy fermionic coherence at "hot spots" of the Fermi surface but coherent
quasiparticles survive in the rest of the Fermi surface. A large part of the
Fermi surface is not really "cold" but rather "lukewarm" in a sense that
coherent quasiparticles in that part survive but are strongly renormalized
compared to the non-interacting case. We discuss the self-energy of lukewarm
fermions and their contribution to the optical conductivity, $\sigma(\Omega)$,
focusing specifically on scattering off composite bosons made of two critical
magnetic fluctuations. Recent study [S.A. Hartnoll et al., Phys. Rev. B {\bf
84}, 125115 (2011)] found that composite scattering gives the strongest
contribution to the self-energy of lukewarm fermions and suggested that this
may give rise to non-Fermi liquid behavior of the optical conductivity at the
lowest frequencies. We show that the most singular term in the conductivity
coming from self-energy insertions into the conductivity bubble,
$\sigma'(\Omega)\propto \ln^3\Omega/\Omega^{1/3}$, is canceled out by the
vertex-correction and Aslamazov-Larkin diagrams. However, the cancelation does
not hold beyond logarithmic accuracy, and the remaining conductivity still
diverges as $1/\Omega^{1/3}$. We further argue that the $1/\Omega^{1/3}$
behavior holds only at asymptotically low frequencies, well inside the
frequency range affected by superconductivity. At larger $\Omega$, up to
frequencies above the Fermi energy, $\sigma'(\Omega)$ scales as $1/\Omega$,
which is reminiscent of the behavior observed in the superconducting cuprates.
