Phase transitions in lattice gauge theories

Research Project, 2025 – 2030

The Yang-Mills theory is an essential model and very active research topic in fundamental physics that describes how particles interact with three of the fundamental forces. Lattice gauge theory (LGT) is a discrete version of this theory, introduced as a means to understand the original (continuous) model. Simulations and heuristic arguments suggest these models exhibit many interesting and important properties. In some cases, these have been verified experimentally, further suggesting that these are useful and physically relevant models. However, very few of these results are supported by rigorous mathematics, and many of the fundamental properties of the model have not yet been understood mathematically. During the last ten years, significant progress have been made on LGTs in the mathematical community. Methods developed for other models continue to be adapted to LGT:s and have revealed a model with many interesting properties that are different from those of similar and more well-studied models such as the Ising model. In particular, there are several phase transitions that appear to be fundamentally different than that of the Ising model. The main goal of this project is to further the understanding about these phase transitions, and ideally be able to describe what happens at the phase transition and in a scaling limit.