三维大$N$标量模型中的行走
Walking in the 3-dimensional large $N$ scalar model
摘要：
三维O（$N$）标量场理论在大$N$极限下的可解性使它成为一个理想的玩具模型，表现出“行走”行为，这在某些具有大量费米子味的SU（$N$）规范理论中是可以预期的。我们使用晶格正则化研究模型，并表明，当粒子质量的有效的4点耦合（与尺寸质量）的比例是小的，与运行的4点耦合的β函数是“行走”。我们还研究了晶格伪影和有限尺寸效应，发现虽然前者可以在现实的相关长度相当大，后者已经在晶格尺寸的几个（$\sim$ 3）相关长度的控制下。我们显示的行走现象的鲁棒性表明，它也可以通过研究物理观测值，如散射相移和有限体积中的质量间隙。
英文摘要：
The solvability of the three-dimensional O($N$) scalar field theory in the large $N$ limit makes it an ideal toy model exhibiting "walking" behavior, expected in some SU($N$) gauge theories with a large number of fermion flavors. We study the model using lattice regularization and show that when the ratio of the particle mass to an effective 4-point coupling (with dimension mass) is small, the beta function associated to the running 4-point coupling is "walking". We also study lattice artifacts and finite size effects, and find that while the former can be sizable at realistic correlation length, the latter are under control already at lattice sizes a few ($\sim$3) correlation lengths. We show the robustness of the walking phenomenon by showing that it can also be observed by studying physical observables such as the scattering phase shifts and the mass gap in finite volume.
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。
