Quantum-critical superconductivity in underdoped cuprates

We argue that the pseudogap phase may be an attribute of the non-BCS pairin g of quantum-critical, diffusive fermions near the antiferromagnetic quantu m critical point. We derive and solve a set of three coupled Eliashberg-typ e equations for spin-mediated pairing and show that in some T range below t he pairing instability, there is no feedback from superconductivity on ferm ionic excitations, and fermions remain diffusive despite of the pairing. We conject that in this regime, fluctuations of the pairing gap destroy the s uperconducting condensate but preserve the leading edge gap in the fermioni c spectral function.