  We study the field theory for the SU($N_c$) symmetric antiferromagnetic
quantum critical metal with a one-dimensional Fermi surface embedded in general
space dimensions between two and three. The asymptotically exact solution valid
in this dimensional range provides an interpolation between the perturbative
solution obtained from the $\epsilon$-expansion near three dimensions and the
nonperturbative solution in two dimensions. We show that critical exponents are
smooth functions of the space dimension. However, physical observables exhibit
subtle crossovers that make it hard to access subleading scaling behaviors in
two dimensions from the low-energy solution obtained above two dimensions.
These crossovers give rise to noncommutativities, where the low-energy limit
does not commute with the limits in which the physical dimensions are
approached.
