  Electronic transport in Fermi liquids is usually Ohmic, because of
momentum-relaxing scattering due to defects and phonons. These processes can
become sufficiently weak in two-dimensional materials, giving rise to either
ballistic or hydrodynamic transport, depending on the strength of
electron-electron scattering. We show that the ballistic regime is a quantum
critical point (QCP) on the regime boundary separating Ohmic and hydrodynamic
transport. The QCP corresponds to a \emph{free} conformal field theory (CFT)
with a dynamical scaling exponent $z = 1$. Its nontrivial aspects emerge in
device geometries with shear, wherein the regime has an intrinsic universal
dissipation, a nonlocal current-voltage relation, and exhibits the critical
scaling of the underlying CFT. The Fermi surface has electron-hole pockets
across all angular scales and the current flow has \emph{vortices} at all
spatial scales. We image the fluctuations in high-definition and animate their
emergence as experimental parameters are tuned to the QCP (movie links in
comments). The vortices clearly demonstrate that Pauli exclusion alone can
produce collective effects, with low-frequency AC transport mediated by vortex
dynamics. The scale-invariant spatial structure is much richer than that of an
interaction-dominated hydrodynamic regime, which only has a single vortex at
the device scale. Our findings provide a theoretical framework for both
interaction-free and interaction-dominated non-Ohmic transport in
two-dimensional materials, as seen in several contemporary experiments.
