  Motivated by the overwhelming evidence some type of quantum criticality
underlies the power-law for the optical conductivity and $T-$linear resistivity
in the cuprates, we demonstrate here how a scale-invariant or unparticle sector
can lead to a unifying description of the observed scaling forms. We adopt the
continuous mass formalism or multi band (flavor) formalism of the unparticle
sector by letting various microscopic parameters be mass-dependent. In
particular, we show that an effective mass that varies with the flavor index as
well as a running band edge and lifetime capture the AC and DC transport
phenomenology of the cuprates. A key consequence of the running mass is that
the effective dynamical exponent can differ from the underlying bare critical
exponent, thereby providing a mechanism for realizing the fractional values of
the dynamical exponent required in a previous analysis\cite{ Hartnoll:2015sea}.
We also predict that regardless of the bare dynamical exponent, $z$, a non-zero
anomalous dimension for the current is required. Physically, the anomalous
dimension arises because the charge depends on the flavor, mass or energy. The
equivalent phenomenon in a $d+1$ gravitational construction is the running of
the charge along the radial direction. The nature of the superconducting
instability in the presence of scale invariant stuff shows that the transition
temperature is not necessarily a monotonic function of the pairing interaction.

Strongly Correlated Electrons;High Energy Physics - Theory