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。这样的预测可以作为表示场论描述的最大有效范围的高能尺度;指示可以，例如，可以由微扰朗道磁极给出，例如在量子电动力学中。到目前为止，基本上所有的粒子物理实验数据都与粒子物理标准模型所提供的量子场理论描述不太一致。然而，扰动估计表明，标准模型有这样一个有限的有效性范围。显然，这是一个没有高能量的完整。类似的结果适用于许多流行的嵌入标准模型到一个更大的量子场论框架。粒子物理模型的关键结构是一个规范汤川系统。实际上，Yukawa规范系统可能有一个最大有效性范围，如标准模型;其他这样的系统可以具有渐近自由的性质。在后一种情况下，所有的相互作用都在高能时消失，相应的模型代表了一个“完美”或高能完备的量子场论，这可能是真正的基本理论。在缺乏最大有效尺度附近的粒子物理数据的情况下，寻找一个完备的理论似乎与事实无关。然而，随着希格斯玻色子的发现和精确的质量测量，标准模型位于一个非常特定的“近临界”参数区域已经变得很清楚。由于这一临界性质与Higgs相互作用势的消失是相容的，渐近自由规范Yukawa模型将不能解释标准模型的近临界性，因此，本研究的目的是寻找和构造渐近自由规范Yukawa系统。目标是对可行的模型进行分类，并分析它们的低能行为，以检查与标准模型质谱的兼容性。作为一个新的和原始的成分，该项目进行了场空间的希格斯势的全球分析。这是强制性的，以揭示可能存在的渐近自由重整化轨迹的微扰理论是盲目的，因为隐含的假设边界条件和渐近对称性。在方法方面，该项目因此提供了新的功能工具，以探索所有理论空间的更大部分，以寻找前所未有的路径，以实现对低能可观测量具有预测能力的高能完整量子场论。

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.