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.

中文翻译：

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通用尺寸的临界费米曲面是由横向规范场相互作用引起的

通过应用先前开发的尺寸正则化方案，我们研究了由有限密度费米子与横向规范场耦合而产生的通用尺寸中的关键费米曲面。版本B 92，035141（2015）]。我们考虑以下情况$ü（\mathrm{1个}）$ 和 $ü（\mathrm{1个}）\times ü（\mathrm{1个}）$横向规范耦合并提取重归一化组（RG）流量固定点的性质以及临界比例。我们的分析使我们能够处理通用尺寸的临界费米表面$米$ 在扩展参数中摄动 $\epsilon =\left(2-米\right)/\left(米+\mathrm{1个}\right)。$ 我们的主要结果之一是，尽管对于某些情况，两环校正不会改变RG流固定线的存在 $ü（\mathrm{1个}）\times ü（\mathrm{1个}）$ 理论，这是较早之前确定的 $米=\mathrm{1个}$以一环的顺序，三阶的图可以。但是，此固定线路功能也可用于$米>\mathrm{1个}$，由于UV / IR混合，答案是精确的一环。