  In recent years it has been shown that strongly coupled systems become
analytically tractable in the regime of large quantum numbers, such as large
spin or large charge. The effective theories that emerge in these two limits
are Regge theory and superfluid theory, respectively. Here we make a proposal
for a new phase, the ``giant vortex,'' describing an intermediate regime with
large spin and charge. The new phase connects superfluid theory with the
large-spin expansion. The giant vortex admits a semi-classical effective theory
description with peculiar chiral excitations (moving at the speed of light) and
a Fock space of states that is reminiscent of the multi-twist operators in
Regge theory, including the leading and daughter Regge trajectories. A similar
giant vortex phase appears for Bose-Einstein condensates in a rotating trap,
and our results should be applicable in that context as well. We show that the
transition from the giant vortex to the Regge regime is accompanied by the
scaling dimension turning from being larger than to being smaller than the mean
field theory value, i.e. gravity switches from being the weakest force at small
AdS distance to being the strongest force at large AdS distance.

High Energy Physics - Theory;Quantum Gases;Strongly Correlated Electrons