Holographic superconductivity of a critical Fermi surface

We construct an emergent geometric description of triplet pairing fluctuations in a two-dimensional metal at a ferromagnetic quantum critical point. The analysis also applies to the behavior of the half-filled lowest Landau level, as well as to other two-dimensional systems featuring emergent gauge fields. Starting from a large-N Yukawa-Sachdev-Ye-Kitaev model of compressible fermions coupled to quantum-critical Ising ferromagnetic fluctuations, we reformulate the pairing problem in terms of bilocal collective fields and analyze Gaussian
fluctuations around the quantum-critical normal state. After projecting onto the dominant low-energy triplet pairing sector, the resulting Gaussian pairing action can be mapped onto a scalar field theory in an emergent curved spacetime with AdS$_2$ ⊗ RS$_2$ geometry. The additional holographic dimension is shown to encode the internal dynamics of Cooper pairs and is related nonlocally to the frequency dependence of the anomalous Gor’kov function via a Radon transform. Within this framework, the onset of superconductivity corresponds
to a Breitenlohner-Freedman instability of the scalar field, which is shown to be equivalent to the pairing instability obtained from the linearized Eliashberg equations. ... mehrThe factorized AdSS$_2$ ⊗ RS$_2$ geometry reflects the local-in-space but critical-in-time character of fermionic excitations near a metallic quantum critical point and corresponds to what one expects in the vicinity of a Reissner-Nordström black hole. Accordingly, our construction establishes a holographic map for the pairing sector of a compressible quantum critical metal and reveals the geometric structure underlying quantum-critical pairing.