Asymptotically free gauged Yukawa systems

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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.