Un-Fermi Liquids: Unparticles in Strongly Correlated Electron Matter

Abstract: Since any non-trivial infrared dynamics in strongly correlated electron matter must be controlled by a critical fixed point, we argue that the form of the single-particle propagator can be deduced simply by imposing scale invariance. As a consequence, the unparticle picture proposed by Georgi\cite{georgi} is the natural candidate to describe such dynamics. Unparticle stuff is scale-invariant matter with no particular mass. Scale invariance dictates that the propagator has an algebraic form which can admit zeros and hence is a candidate to explain the ubiquitous pseudogap state of the cuprates. The non-perturbative electronic state formed out of unparticles we refer to as an un-Fermi liquid. We show that the underlying action of the continuous mass formulation of unparticles can be recast exactly as an action in anti de Sitter space. We find that this mapping fixes the scaling dimension of the unparticle to be $d_U=d/2+\sqrt{d^2+4}/2$ and ensures that the corresponding propagator has zeros with $d$ the spacetime dimension of the unparticle field. Should $d=2+1$, unparticles acquire the non-trivial phase $2\pi d_U$ upon interchange. Because $d_U$ is non-integer and in general not half-integer, clockwise and counterclockwise interchange of unparticles do not lead to the same phase and time reversal symmetry is broken spontaneously as reported in numerous experiments in the pseudogap phase of the cuprates. The possible relevance of this mechanism to such experiments is discussed. We then formulate the analogous BCS gap using unparticles and find that in contrast to the Fermi liquid case, the transition temperature increases as the attractive interaction strength decreases, indicating that unparticles are highly susceptible to a superconducting instability.