Interplay between superconductivity and non-Fermi liquid at a quantum-critical point in a metal. IV: The $\gamma$ model and its phase diagram at $1<\gamma <2$

In this paper, we continue our analysis of the interplay between pairing and non-Fermi liquid behavior for a set of itinerant quantum-critical systems with an effective dynamical electron-electron interaction $V(\Omega_m) \propto 1/|\Omega_m|^\gamma$ (the $\gamma$-model). In previous papers, we considered the cases $0 1$, and the imaginary part $V^{''} (\Omega) \propto \sin(\pi \gamma/2)/|\Omega|^\gamma$ decreases as $\gamma \to 2$.