Noncommutativity between the low-energy limit and integer dimension limits in the ε expansion: A case study of the antiferromagnetic quantum critical metal

We study the field theory for the SU(Nc) 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 ε expansion near three dimensions and the nonperturbative solution in two dimensions. We show that critical …