Speaker: Gian Andrea Inkof

Affiliation:
Karlsruhe Institute of Technology

Title:
Superconductivity in SYK models

Abstract:
The tendency of non-Fermi liquid states towards superconductivity through pairing of fermionic excitations is complicated by the disappearance of quasi-particles at strong coupling. Recently solvable SYK-like models of randomly interacting phonons and complex fermions in (0+1)-dimensions have been shown to match many of the properties of non-Fermi liquid superconductors. Superconductivity is better understood in higher dimensional models. We embed the phonon-fermion dot in a d-dimensional lattice and derive the effective action for collective fields. Near the saddle point, the model is governed by a phase field which is conjugated to charge fluctuations and impacts superconducting properties. At low energies the system is strongly coupled and is conjectured to have a gravitational dual. We discuss putative holographic theories able to match the IR behavior of the random phonon-fermion gas.