四维以上规范理论中的渐近安全：微扰测试与不动点合并

中文摘要 AI 辅助

四维以上的非阿贝尔规范理论可通过正则标度与规范场反屏蔽的竞争，存在相互作用型紫外不动点。利用延拓至D=4+2ε的四圈overline{MS}β函数，我们确定了满足特定比率准则时，不动点的逐圈修正仍保持层级有序的最大维度D_{pt}=4+2ε_{pt}，并针对SU(N)基础表示下的费米子，绘制了D_{pt}随色荷数与味荷数的变化图。在D=5维下，我们借鉴泛函重整化群（fRG）构造了带有固定极点正则化分母的有理反常维数。通过与overline{MS}级数的一圈、两圈、三圈匹配，紫外-红外合并点（红外与紫外不动点重合的点）处的临界味荷数与耦合常数的偏移量逐步减小，三圈构造下大N极限的N_f^{cr}≈2.09N。这种低阶稳定化，结合包含高阶规范算子的fRG流的定性证据，提出了一种潜在的合并场景，该场景以味荷数为界约束候选渐近安全区域。所得色-味图既给出了微扰控制的基线边界，也给出了候选三圈合并边界，为五维模型构建提供了指导。然而，四圈匹配在三圈合并边界之外仍保留相互作用型紫外不动点，在整数2≤N≤15且0≤N_f/N≤11/2的范围内未发现合并。不动点结构对高阶项的敏感性使得两种场景均成立，凸显了不动点湮灭可作为五维渐近安全的潜在约束。

英文摘要

Non-Abelian gauge theories above four dimensions may admit an interacting ultraviolet fixed point through the competition between canonical scaling and gauge-field antiscreening. Using the four-loop $\overline{\mathrm{MS}}$ beta function continued to $D=4+2ε$, we determine the largest dimension $D_{\mathrm{pt}}=4+2ε_{\mathrm{pt}}$ below which successive loop corrections to the fixed point remain hierarchically ordered under a specified ratio criterion, and map $D_{\mathrm{pt}}$ over color and flavor numbers for fermions in the fundamental representation of $SU(N)$. At $D=5$, we construct rational anomalous dimensions with a fixed, pole-regularized denominator inspired by the functional renormalization group (fRG). Matching to the $\overline{\mathrm{MS}}$ series through one, two, and three loops produces progressively smaller shifts in the critical flavor number and coupling at the ultraviolet--infrared merger (the point where the infrared and ultraviolet fixed points coincide), yielding $N_f^{\mathrm{cr}}\simeq 2.09 \, N$ at large $N$ in the three-loop construction. This low-order stabilization, together with qualitative evidence from fRG flows including higher gauge operators, suggests a potential merger scenario that bounds the candidate asymptotically safe region in flavor number. The resulting color--flavor map provides guidance for five-dimensional model building by displaying both the baseline perturbative-control boundary and the candidate three-loop merger boundary. Four-loop matching, however, retains an interacting ultraviolet fixed point beyond the three-loop merger boundary, with no merger found for integer $2\le N\le15$ and $0\le N_f/N\le11/2$. The sensitivity of the fixed-point structure to higher-order terms leaves both scenarios open, highlighting fixed-point annihilation as a potential constraint on five-dimensional asymptotic safety.

发表机构

• Université Lyon 1, CNRS, IP2I（里昂第一大学）
• University of Johannesburg（约翰内斯堡大学）
• The University of Electronic Science and Technology of China（电子科技大学）
• Lund University（隆德大学）

机构由 AI 辅助整理，请以论文原文为准。

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13 pages, 8 figures