  We study the dynamic response of a two-dimensional system of itinerant
fermions in the vicinity of a uniform ($\mathbf{Q}=0$) Ising nematic quantum
critical point of $d-$wave symmetry. The nematic order parameter is not a
conserved quantity, and this permits a nonzero value of the fermionic
polarization in the $d-$wave channel even for vanishing momentum and finite
frequency: $\Pi(\mathbf{q} = 0,\Omega_m) \neq 0$. For weak coupling between the
fermions and the nematic order parameter (i.e. the coupling is small compared
to the Fermi energy), we perturbatively compute $\Pi (\mathbf{q} = 0,\Omega_m)
\neq 0$ over a parametrically broad range of frequencies where the fermionic
self-energy $\Sigma (\omega)$ is irrelevant, and use Eliashberg theory to
compute $\Pi (\mathbf{q} = 0,\Omega_m)$ in the non-Fermi liquid regime at
smaller frequencies, where $\Sigma (\omega) > \omega$. We find that
$\Pi(\mathbf{q}=0,\Omega)$ is a constant, plus a frequency dependent correction
that goes as $|\Omega|$ at high frequencies, crossing over to $|\Omega|^{1/3}$
at lower frequencies. The $|\Omega|^{1/3}$ scaling holds also in a non-Fermi
liquid regime. The non-vanishing of $\Pi (\mathbf{q}=0, \Omega)$ gives rise to
additional structure in the imaginary part of the nematic susceptibility
$\chi^{''} (\mathbf{q}, \Omega)$ at $\Omega > v_F q$, in marked contrast to the
behavior of the susceptibility for a conserved order parameter. This additional
structure may be detected in Raman scattering experiments in the $d-$wave
geometry.
