arXiv 2402.178172024-02hep-thcond-mat.stat-mechhep-ph

微扰多重标量重整化群流的梯度性质至六圈阶

Gradient Properties of Perturbative Multiscalar RG Flows to Six Loops

William H. Pannell, Andreas Stergiou

备注：: 8 pages (two-column), 2 figures, ancillary files are included containing constraints, beta function and additional conventions. v2 discussion expanded including an additional appendix with an explicit solution through two loops, accepted for publication in Physics Letters B

阅读 PDF

arXiv 页面 ↗HTML 原文 ↗

AI总结：

本文研究多重标量理论重整化群流的梯度性质，发现修正后的B函数在五圈内为梯度场，而传统beta函数在六圈时不再具有梯度性质，并给出了六圈梯度条件。

摘要：

本文在 $d=4$ 和 $d=4-\varepsilon$ 维度下，对多重标量理论的重整化群（RG）流的梯度性质进行了微扰检验。此类理论在四次耦合 $\lambda^I$ 空间中经历重整化群流。从五圈开始，决定物理重整化群流的相关矢量场并不是传统上在维度正规化的最小减除方案中计算的 beta 函数，而是对其进行了适当修正后的 $B$ 函数。研究发现，直到五圈，$B$ 矢量场是梯度场，即 $B^I=G^{IJ}\partial A / \partial \lambda^J$，其中 $A$ 是一个标量，$G_{IJ}$ 是耦合常数的二阶对称张量。直到五圈，beta 函数也是梯度场，但在六圈时不再满足梯度性质。本文给出了 $B$ 函数（因而重整化群流）在六圈时具有梯度性质所需满足的条件，但这些条件的验证依赖于一项尚未完成的独立的六圈计算。

英文摘要：

The gradient property of the renormalisation group (RG) flow of multiscalar theories is examined perturbatively in $d=4$ and $d=4-\varepsilon$ dimensions. Such theories undergo RG flows in the space of quartic couplings $λ^I$. Starting at five loops, the relevant vector field that determines the physical RG flow is not the beta function traditionally computed in a minimal subtraction scheme in dimensional regularisation, but a suitable modification of it, the $B$ function. It is found that up to five loops the $B$ vector field is gradient, i.e. $B^I=G^{IJ}\partial A / \partialλ^J$ with $A$ a scalar and $G_{IJ}$ a rank-two symmetric tensor of the couplings. Up to five loops the beta function is also gradient, but it fails to be so at six loops. The conditions under which the $B$ function (and hence the RG flow) is gradient at six loops are specified, but their verification rests on a separate six-loop computation that remains to be performed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

AI总结：

摘要：

英文摘要：

相关论文