论文标题
能量弹药张量的位置空间重量级化
Position-Space Renormalisation of the Energy-Momentum Tensor
论文作者
论文摘要
研究三维量子场理论（QFT）的非扰动方面的研究越来越兴趣。它们是（强耦合）重力理论的全息双重偶。例如，在全息宇宙学中，可以将特定类别三维QFT的能量弹药张量（EMT）的两点函数映射到引力理论中宇宙微波背景的功率谱。然而，在晶格上提取重量化的EMT两点函数时，发散的接触项的存在引起了挑战。使用$ \ Mathfrak {su}（n）$的$ ϕ^4 $的伴随标量理论，作为由全息宇宙学动机的概念证明，我们采用了一种新颖的方法来滤除此类接触术语，通过无限不同的“ bump”功能来强制换成零用范围的零用窗口，从而使Zero贡献了零件的零用零件。该过程有效地删除了本地接触项，并允许我们提取重量化的EMT两点函数的连续限制行为。
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.
