Multiple solutions for superconductivity at T=0 in a quantum-critical metal*

We discuss the interplay between non-Fermi liquid behaviour and superconductivity at a quantum-critical point (QCP) in a metal. It is widely thought that the tendency towards superconductivity and towards non-Fermi liquid behaviour compete with each other, and if the pairing interaction is reduced below a certain threshold, the system displays a naked non-Fermi liquid QC behaviour. We show that at T=0 there is indeed a threshold below which the system remains in the normal state. We argue that above the threshold the system develops a discrete, but infinite set of solutions for the pairing gap. In particular, for ant value of the pairing interaction above the threshold there exists a solution of the linearized gap equation. This is very different from a conventional superconductivity, when the solution of the linearized gap equation exists only a critical strength of the pairing interaction. We present some exact results the set of QC models with frequency-dependent effective interaction and discuss the consequences of the existence of multiple solutions for superconductivity at a QCP.