The role of superconducting fluctuations in the Yukawa-SYK model

The Yukawa-SYK (YSYK) model describing a system of correlated electrons randomly coupled to bosons has recently attracted much attention due to its resemblance to strange metals. It further allows for incorporating electron-phonon-like superconductivity in the same traceable framework, making the YSYK model a promising asset for qualitative studies of strange metal/superconductor transition. Yet, the properties of the metallic sector of the system may be impacted by the fluctuations of the superconducting order parameter conventionally accounted for perturbatively. We show that the YSYK model possesses unconventional behavior of superconducting order parameter fluctuations. We argue that in the case of the YSYK model, superconducting fluctuations play a substantial role in the formation of the large-N saddle point solution of the model, which may lead to important non-perturbative effects in the metallic regime.