Pairing Instability on a Luttinger Surface: A Non-Fermi Liquid to Superconductor Transition and its SYK Dual

Instabilities of the Fermi Surface -- contours of poles of the single particle Green function -- such as superconductivity, density waves (CDW, SDW, PDW..) etc are now a commonplace in modern condensed matter physics. In this talk, I will discuss the problem of superconducting instability on a model Luttinger surface, or contours of zeros of the many-body Green function.

Unlike a Fermi surface, in the presence of an attractive potential, the model exhibits -- in the strong coupling limit -- a quantum phase transition into a superconducting state. The spectral density of pair fluctuations in the "normal" state of the superconductor has a power-law type van-Hove singularity signalling non-Fermi liquid transport. Crucially, the fluctuation free energy in the non-Fermi liquid resembles well-studied models with gravity duals such as SYK. These results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mottness and strongly coupled toy-models exhibiting gravity duals.