AI 中文总结
本研究将软共线有效理论框架应用于几何标量场理论，构建geoSCET模型，推导其几何软定理，证明无势理论满足普适几何软定理，且引入软能标势不破坏软物理因子化，揭示几何软定理的场空间微分同胚起源。
AI 中文摘要
我们将软共线有效理论（SCET）框架应用于几何标量场理论，所得的“geoSCET”在软区呈现出涌现几何，与量子色动力学软共线有效理论（QCD SCET）的涌现软规范不变性类似。我们利用geoSCET推导几何软定理，将其作为有效场论幂次计数的直接结果，包括对多重软辐射和圈修正的扩展。我们证明，无势理论对任意数量的软辐射、到微扰论的所有阶均满足普适几何软定理；还表明，在软能标下引入势不会破坏软物理的因子化。本工作揭示了几何软定理的 underlying 场空间微分同胚起源。
英文摘要
We apply the framework of Soft Collinear Effective Theory (SCET) to the theory of the geometric scalar field. The resulting ``geoSCET'' manifests an emergent geometry in the soft sector, mirroring the emergent soft gauge invariance of QCD SCET. We use geoSCET to derive the geometric soft theorems as straightforward consequences of effective-field-theory power counting, including extensions to multiple soft emissions and loop corrections. We demonstrate that theories without a potential satisfy universal geometric soft theorems for any number of soft emissions to all orders in perturbation theory. We also show that we can turn on a potential at the soft scale without spoiling the factorization of the soft physics. This work demonstrates the underlying field-space diffeomorphism origin of the geometric soft theorem.
Comments69 pages, 5 figures
