  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.
