  This paper is a continuation and a partial summary of our analysis of the
pairing at a quantum-critical point (QCP) in a metal for a set of
quantum-critical systems, whose low-energy physics is described by an effective
model with dynamical electron-electron interaction $V(\Omega_m) = ({\bar
g}/|\Omega_m|)^\gamma$ (the $\gamma$-model). Examples include pairing at the
onset of various spin and charge density-wave and nematic orders and pairing in
SYK-type models. In previous papers, we analyzed the physics for $\gamma <2$.
We have shown that the onset temperature for the pairing $T_p$ is finite, of
order ${\bar g}$, yet the gap equation at $T=0$ has an infinite set of
solutions within the same spatial symmetry. As the consequence, the
condensation energy $E_c$ has an infinite number of minima. The spectrum of
$E_c$ is discrete, but becomes more dense as $\gamma$ increases. Here we
consider the case $\gamma =2$. The $\gamma=2$ model attracted special interest
in the past as it describes the pairing by an Einstein phonon in the limit when
the dressed phonon mass $\omega_D$ vanishes. We show that for $\gamma =2$, the
spectrum of $E_c$ becomes continuous. We argue that the associated gapless
"longitudinal" fluctuations destroy superconducting phase coherence at a finite
$T$, such that at $0<T< T_p$ the system displays pseudogap behavior. We show
that for each gap function from the continuum spectrum, there is an infinite
array of dynamical vortices in the upper half-plane of frequency. For the
electron-phonon case at a finite $\omega_D$, our results show that $T_p =0.1827
{\bar g}$, obtained in earlier studies, marks the onset of the pseudogap
behavior, while the actual superconducting $T_c$ scales with $\omega_D$ and
vanishes at $\omega_D \to 0$.
