基于物理信息神经网络的Higgs单态模型非微扰泛函重整化群
Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks
浏览论文内容
中文总结 AI 辅助
本文提出基于物理信息神经网络的非微扰泛函重整化群方法，求解Higgs单态模型有效势，无需多项式展开，并应用于电弱相变分析，发现软一致性约束对选择物理解至关重要。
中文摘要 AI 辅助
我们在LPA'框架内发展了一个非微扰泛函重整化群框架，用于在零温和有限温度下求解标准模型的$Z_2$对称实单态扩展的Wetterich流方程，无需对尺度依赖的有效势进行多项式展开，而是采用物理信息神经网络（PINN）表示。与基于低阶场展开的传统截断相比，我们的树级加神经网络混合ansatz在完整的相关场和尺度范围内提供了有效势的连续、无网格描述。作为概念验证，我们将该框架应用于与该模型中电弱相变相关的有限温度有效势：两个基准温度下的一维场空间切片，以及在$T=100$ GeV下的二维重构，从中提取了两步反弹作用。重整化群流在尺度和场空间的多域设置中实现，并采用导数匹配条件以确保平滑性和数值稳定性。规范场和Yukawa扇区通过独立计算的微扰两环跑动耦合纳入，反常维度在LPA'水平上包含在流中。我们将网络与重求和微扰理论以及同一方程的基于网格的松弛求解器进行基准比较。最后，我们引入一个软一致性约束，使解在场空间域内与微扰理论在符号和数量级上保持接近；我们发现该约束对于选择流方程的物理上合理的解是必要的，而不仅仅是辅助性的，并发现收敛结果对该引导（通过手动调整的权重和分析热目标）保留了残余依赖性，我们将其确定为核心开放问题。
英文摘要
We develop a nonperturbative functional renormalization group framework within the LPA' to solve the Wetterich flow equation for the $Z_2$-symmetric real singlet extension of the Standard Model at finite temperature, without a low-order polynomial truncation of the loop corrections to the effective potential, using a physics-informed neural network (PINN) representation. In contrast to conventional truncations based on low-order field expansions, our hybrid tree-level-plus-neural-network ansatz yields a continuous, mesh-free description of the effective potential over the full field and scale range. As a proof of concept, we apply the framework to the finite-temperature effective potential relevant to the electroweak phase transition: one-dimensional field-space slices at two benchmark temperatures, and a two-dimensional reconstruction at T=100 GeV yielding a two-step bounce action. The flow is implemented in a multi-domain setup in scale and field space with derivative matching conditions ensuring smoothness and numerical stability. Gauge and Yukawa sectors are incorporated via independently computed perturbative two-loop running couplings, and anomalous dimensions are included in the flow at the LPA' level. We benchmark the network against resummed perturbation theory and against a grid-based relaxation solver of the same equation. Finally, we introduce a soft consistency constraint that keeps the solution close, in sign and order of magnitude, to perturbation theory across the field-space domain. We find this constraint necessary, rather than merely helpful, for selecting a physically sensible solution of the flow equation. The converged result nevertheless retains a residual dependence on this guidance -- through hand-tuned weights and an analytic thermal target -- which we identify as the central open problem for mesh-free FRG treatments of this kind.
发表机构
- Zhejiang Institute of Modern Physics and Department of Physics, Zhejiang University（浙江大学现代物理研究所和物理学院）
机构由 AI 辅助整理，请以论文原文为准。
