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 $U\left(1\right)$ and $U\left(1\right)\times U\left(1\right)$ 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 $\epsilon =\left(2-m\right)/\left(m+1\right).$ 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 $U\left(1\right)\times U\left(1\right)$ 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.

• Received 18 June 2020
• Revised 7 November 2020
• Accepted 10 November 2020
• Corrected 29 July 2021

DOI:https://doi.org/10.1103/PhysRevResearch.2.043277

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Published by the American Physical Society