Critical Fermi surfaces in generic dimensions arising from transverse gauge field interactions

We study critical Fermi surfaces in generic dimensions arising from coupling finite-density fermions with transverse gauge fields by applying a dimensional regularization scheme developed previously [Phys. Rev. B 92, 035141 (2015)]. We consider the cases of U(1) and U(1) xU(1) transverse gauge couplings and extract the nature of the renormalization group (RG) flow fixed points as well as the critical scalings. Our analysis allows us to treat a critical Fermi surface of a generic dimension m perturbatively in an expansion parameter epsilon = ( 2 - m)/(m + 1). One of our key results is that although the two-loop corrections do not alter the existence of an RG flow fixed line for certain U(1) xU(1) theories, which was identified earlier for m = 1 at one-loop order, the third-order diagrams do. However, this fixed line feature is also obtained for m > 1, where the answer is one-loop exact due to UV/IR mixing.