Abstract

The theory of superconductivity in strongly-correlated, quantum-critical systems is a great challenge in condensed matter physics. The Bardeen-Cooper-Schrieffer paradigm is indeed invalidated by the strong interactions and the absence of quasi-particles. This behavior is typical of systems where pairing is caused by magnetic or Ising nematic quantum critical fluctuations, color magnetic interaction in high-density quark matter, or where it occurs in U(1) and Z2 spin-liquid states. To tackle these problems, two very different formalisms have been developed: holographic superconductivity and quantum-critical Eliashberg theory. The former exploits the duality between quantum field theories and gravity theories, while the latter includes a strongly retarded pairing interaction of ill-defined fermions.
In the first part of this seminar, I will review the basics of the AdS/CFT conjecture and holographic superconductivity. Examples of systems with a gravity dual are N = 4 super Yang-Mills theories and the (0+1)-dimensional model of Sachdev-Ye-Kitaev (SYK). In the second part, I will introduce a generalization of SYK described by quantum critical Eliashberg equations and I will explicitly derive holography out of it. Having shown that the two approaches map onto each other, we then exploit the power of holography to determine the dynamic pairing susceptibility of the model. Our holographic map constitutes a concrete example where the correspondence holds exactly in a system with a much lower degree of symmetry.