Title: Interplay Between  Superconductivity and Non-Fermi Liquid at a QCP in a Metal
Abstract: I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal.  These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter.  The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence.  I discuss this physics for a class of models with an effective dynamical interaction V (W) ~1/|W|^g (the g-model).   This model describes, in particular, the pairing at a 2D Ising-nematic critical point (g=1/3), a 2D  antiferromagnetic critical point (g=1/2) and the pairing by  an Einstein phonon with vanishing dressed Debye frequency (g=2).    I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops pseudo-gap behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp   decreases with g and vanishes at g =2.  I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at g =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at g =2.   I argue that a fundamentally novel superconducting ground state emerges at g >2.