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

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