Asymptotically free gauged Yukawa systems

量子场论在物理理论中提供了一个独特的性质：它可以预测自己的崩溃。这样的预测可以是代表场论描述的最大有效范围的高能标度；例如，可以由微扰朗道极给出指示，例如在量子电动力学中。基本上，到目前为止所有的实验粒子物理数据与粒子物理标准模型提供的量子场理论描述并不是非常精确。然而，微扰估计表明，标准模型的有效范围是如此有限。显然，它并不是完全的高能。类似的结果适用于许多流行的将标准模型嵌入到更大的量子场论框架中的情况。粒子物理模型的关键结构是巨型汤川系统的结构。事实上，测量的汤川系统可能有一个最大有效范围，如标准模型；其他此类系统可以具有渐近自由的性质。在后一种情况下，所有的相互作用都会朝着高能方向消失，而相应的模型代表了一个“完美的”或高能完全的量子场理论，这可能是真正的基础。在缺乏接近表观最大有效性标度的粒子物理数据的情况下，寻找一个完整的理论在事实上似乎不那么重要。然而，随着希格斯玻色子的发现及其精确的质量测量，很明显，标准模型位于一个非常具体的“近临界”参数区域。由于这一临界性性质与消失的Higgs相互作用势相容，渐近自由的规范汤川模型将从理论上解释标准模型的近临界性。因此，目前提出的寻找和构建渐近自由汤川系统的建议受到概念一致性和实验数据的推动。我们的目标是对可行的模型进行分类，并分析它们的低能量行为，以检查与标准模型质谱图的兼容性。作为一种新的原创成分，该项目对场空间中的希格斯势进行了全球分析。这是强制性的，以揭示由于边界条件和渐近对称性的隐含假设，微扰理论对渐近自由化轨迹的可能存在是盲目的。因此，在方法方面，该项目提供了新的功能工具，以探索所有理论空间中相当大的一部分，以便寻找前所未有的途径，获得具有对低能量可观测性的预测能力的高能完整量子场理论。

Quantum field theory offers a unique property among physical theories:it can predict its own breakdown. Such a prediction can come as ahigh-energy scale representing a maximum validity range of the fieldtheory description; indications can, e.g., be given by perturbative Landaupoles, such as in quantum electrodynamics. Essentially all experimental particle physics data so far is inremarkably precise agreement with the quantum field theoreticaldescription provided by the Standard Model of particlephysics. Nevertheless, perturbative estimates suggest that theStandard Model has such a limited validity range. Apparently, it is nothigh-energy complete. Similar results hold for many popular embeddingsof the Standard Model into a larger quantum field theory framework.The key structure of particle physics models is that of a gaugedYukawa system. In fact, gauged Yukawa systems may have a maximumvalidity range such as the Standard Model; other such systems canfeature the property of asymptotic freedom. In the latter case, allinteractions vanish towards high energies and the corresponding modelrepresents a "perfect" or high-energy-complete quantum field theorywhich could be truly fundamental.In absence of particle physics data near the apparent maximum validityscale, the search for a complete theory seems factually lessrelevant. Nevertheless, with the discovery of the Higgs boson and itsprecise mass measurement, it has become clear that the Standard Modellies in a very specific "near-critical" parameter region. Since thiscriticality property is compatible with a vanishing Higgsinteraction potential, asymptotically free gauged Yukawa models wouldintrinsically explain the near-criticality of the Standard Model.The present proposal to search for and construct asymptotically freegauged Yukawa systems is hence motivated by conceptual consistency aswell as experimental data. The goal is to classify viable models andto analyze their low-energy behavior to check for compatibility withthe Standard Model mass spectrum. As a new and original ingredient, the project performs a globalanalysis of the Higgs potential in fields space. This is mandatory inorder to unveil the possible existence of asymptotically freerenormalization trajectories to which perturbation theory is blind,because of implicit assumptions on boundary conditions and asymptoticsymmetry. On the method side, the project thus provides new functionaltools to explore a substantially larger section of the space of alltheories in order to search for unprecedented routes to high-energycomplete quantum field theories with predictive power for low-energyobservables.