  We study the problem of disorder-free metals near a continuous Ising nematic
quantum critical point in $d=3+1$ dimensions. We begin with perturbation theory
in the `Yukawa' coupling between the electrons and undamped bosons (nematic
order parameter fluctuations) and show that the perturbation expansion breaks
down below energy scales where the bosons get substantially Landau damped.
Above this scale however, we find a regime in which low-energy fermions obtain
an imaginary self-energy that varies linearly with frequency, realizing the
`marginal Fermi liquid' phenomenology\cite{Varma}. We discuss a large N theory
in which the marginal Fermi liquid behavior is enhanced while the role of
Landau damping is suppressed, and show that quasiparticles obtain a decay rate
parametrically larger than their energy.
