Gauge gravity duality for d-wave superconductors: prospects and challenges

TL;DR

This paper develops a holographic model using a charged, massive spin-two field in AdS space to study d-wave superfluid phase transitions and their properties within the gauge/gravity duality framework.

Contribution

It proposes a new effective field theory approach to model d-wave superconductors using a spin-two field in AdS, addressing technical challenges and exploring phase diagram and conductivity.

Findings

Phase diagram of the superfluid phase mapped out.

Charge conductivity behavior analyzed.

Effects of fermion couplings on spectral functions discussed.

Abstract

We write down an action for a charged, massive spin two field in a fixed Einstein background. Despite some technical problems, we argue that in an effective field theory framework and in the context of the AdS/CFT correspondence, this action can be used to study the properties of a superfluid phase transition with a d-wave order parameter in a dual strongly interacting field theory. We investigate the phase diagram and the charge conductivity of the superfluid phase. We also explain how possible couplings between the spin two field and bulk fermions affect the fermion spectral function.