Unparticles and Fermi Arcs in the Cuprates

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One of the open problems in strong correlation physics is whether or not
Luttinger's theorem works for doped Mott insulators, particularly in
the pseudo gap regime where the pole-like excitations form only a Fermi
arc. I will begin this talk by using this theorem to count particles and
show that it fails in general for the Mott state. The failure stems
from the divergent self energy that underlies Mottness. When such a
divergence is present, charged degrees of freedom are present that have
no particle interpretation. I will argue that such excitations are
governed by a non-trivial IR fixed point and the propagator of which is
of the unparticle form proposed by Georgi. I will show how a gravity
dual can be used to determine the scaling dimension of the unparticle
propagator. I will close by elucidating a possible superconducting
instability of unparticles and demonstrate that unparticle stuff is
likely to display fractional statistics in the dimensionalities of
interest for strongly correlated electron matter.  Time permitting, an
underlying theory of the strongly coupled fixed point will be outlined.