2D or not 2D? (Large N dimensional reduction of Lowest Landau Level physics)

We show that for a large number N of 2D fermions in the lowest
Landau level (LLL), the fermion density satisfies an upper bound,
reminiscent of 1D physics. We discuss the relation between this
"dimensional reduction" and the classical notion of non-commutativity
arising from the LLL constraints. We show how dynamics of the 2D LLL
fermions is simplified by the 1D description. We also discuss the EE of a
2D subregion; the EE follows neither a 2D formula nor a 1D formula but
something in between, We briefly mention a possible application to
fractional Quantum Hall Effect. We also discuss the relation between this
model and matrix model and string theory.