德国慕尼黑工业大学Dominik Haslehner团队近日研究了重整场空间几何。该项研究成果发表在2025年7月15日出版的《高能物理杂志》上。
研究组从几何角度系统地研究了标量有效场论中的单环量子修正，强调了场空间曲率及其重整化的作用。通过将标量场视为黎曼流形上的坐标，利用场重定义不变性来保持物理可观测值的明显坐标独立性。在非线性sigma模型（NLSM）和Φ4理论的聚焦下，研究组展示了环路修正如何在场空间流形的曲率中诱导动量和尺度相关的位移。这些修正可以通过最近提出的几何运动学对偶来精细捕捉，该对偶将规范理论中的颜色运动学对偶推广到弯曲的场空间背景。
该结果强调了在黎曼张量的收缩中出现的普遍结构，这有助于场空间曲率的重整化。特别是，研究组在简单模型中找到了运行曲率和里奇标量的显式表达式和通用结构，说明了量子效应如何重塑底层几何。这个几何公式统一了一大类标量，提供了对曲率、散射振幅和重整化的相互作用的见解。
附：英文原文
Title: Renormalising the field-space geometry
Author: Aigner, Patrick, Bellafronte, Luigi, Gendy, Emanuele, Haslehner, Dominik, Weiler, Andreas
Issue&Volume: 2025-07-15
Abstract: We present a systematic study of one-loop quantum corrections in scalar effective field theories from a geometric viewpoint, emphasizing the role of field-space curvature and its renormalisation. By treating the scalar fields as coordinates on a Riemannian manifold, we exploit field redefinition invariance to maintain manifest coordinate independence of physical observables. Focusing on the non-linear sigma model (NLSM) and 4 theory, we demonstrate how loop corrections induce momentum- and scale-dependent shifts in the curvature of the field-space manifold. These corrections can be elegantly captured through the recently proposed geometry-kinematics duality, which generalizes the colour-kinematics duality in gauge theories to curved field-space backgrounds. Our results highlight a universal structure emerging in the contractions of Riemann tensors that contribute to renormalisation of the field-space curvature. In particular, we find explicit expressions and a universal structure for the running curvature and Ricci scalar in simple models, illustrating how quantum effects reshape the underlying geometry. This geometric formulation unifies a broad class of scalar EFTs, providing insight into the interplay of curvature, scattering amplitudes, and renormalization.
DOI: 10.1007/JHEP07(2025)167
Source: https://link.springer.com/article/10.1007/JHEP07(2025)167