能量动量张量的位置空间重整化
Position-Space Renormalisation of the Energy-Momentum Tensor
摘要：
三维量子场论（QFT）的非微扰性研究日益受到人们的关注。它们表现为（强耦合）引力理论的全息对偶。例如，在全息宇宙学中，一类特殊的三维量子场论的能量动量张量（EMT）的两点函数可以映射到引力理论中的宇宙微波背景的功率谱中。然而，存在分歧的接触条款提出了挑战，在提取重整化的EMT两点函数的晶格。使用$ϕ^4$理论的伴随标量值的$\mathfrak{su}(N)$李代数作为全息宇宙学的动机的概念证明，我们采用了一种新的方法，通过利用无限可微的“凸点”功能，强制执行一个光滑的窗口，排除在零空间分离的贡献过滤出这样的接触条款。该过程有效地消除了当地的接触条款，并允许我们提取的连续极限行为的重整化EMT两点函数。
英文摘要：
There is increasing interest in the study of nonperturbative aspects of three-dimensional quantum field theories (QFT). They appear as holographic dual to theories of (strongly coupled) gravity. For instance, in Holographic Cosmology, the two-point function of the Energy-Momentum Tensor (EMT) of a particular class of three-dimensional QFTs can be mapped into the power spectrum of the Cosmic Microwave Background in the gravitational theory. However, the presence of divergent contact terms poses challenges in extracting a renormalised EMT two-point function on the lattice. Using a $ϕ^4$ theory of adjoint scalars valued in the $\mathfrak{su}(N)$ Lie Algebra as a proof-of-concept motivated by Holographic Cosmology, we apply a novel method for filtering out such contact terms by making use of infinitely differentiable "bump" functions which enforce a smooth window that excludes contributions at zero spatial separation. The process effectively removes the local contact terms and allows us to extract the continuum limit behaviour of the renormalised EMT two-point function.
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。
