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Models for strongly interacting fermions in disordered clusters forming anarray, with electron hopping between sites, reproduce the linear dependence ontemperature of the resistivity, typical of the strange metal phase of HighTemperature Superconducting materials (Extended Sachdev-Ye-Kitaev (SYK)models). Our hydrodynamical approach to the marginal Fermi liquid emerging outof the interaction, identifies the low energy collective excitations of thesystem in its coherent phase. These neutral excitations diffuse in the lattice,but the diffusion is heavily hindered by coupling to the pseudo Goldstone modesof the conformal broken symmetry SYK phase, which are local in space. Acritical temperature for superconductivity arises in the electron liquid,incase these excitations are assumed to mediate an attractive Cooper-pairing, inthe electron liquid, which is not BCS-like.

Superconducting critical temperature in the extended diffusive SYK model