  The two-dimensional Yukawa-Sachdev-Ye-Kitaev (2d-YSYK) model provides a
universal theory of quantum phase transitions in metals in the presence of
quenched random spatial fluctuations in the local position of the quantum
critical point. It has a Fermi surface coupled to a scalar field by spatially
random Yukawa interactions. We present full numerical solutions of a
self-consistent disorder averaged analysis of the 2d-YSYK model in both the
normal and superconducting states, obtaining electronic spectral functions,
frequency-dependent conductivity, and superfluid stiffness. Our results
reproduce key aspects of observations in the cuprates as analyzed by Michon et
al. (arXiv:2205.04030). We also find a regime of increasing zero temperature
superfluid stiffness with decreasing superconducting critical temperature, as
is observed in bulk cuprates.
