Holographic superconductivity of a critical Fermi surface

Abstract: We derive holographic superconductivity from a Hamiltonian that describes pairing of two-dimensional electrons near a ferromagnetic quantum-critical point. At low energies the theory maps onto a four-dimensional gravity description with Lifshitz spacetime and dynamic scaling exponent $z=3/2$. The curved spacetime is due to powerlaw correlations of the critical normal state. The Lifshitz anisotropy is caused by phase-space constraints near the Fermi surface. The pairing instabilities obtained in Lifshitz space and from the Eliashberg formalism are found to be identical. We also formulate the holographic map for values of the dynamic scaling exponent $1<z<\infty$. Our result provides an explicit realization of the holographic correspondence in two dimensions.