Finding All Integrable Models

Introduction

Symmetry plays an important role in our current understanding of nature. For instance, in the development of the Standard Model of particle physics, the understanding of the gauge group of symmetries was crucial. There is a class of models, called integrable systems, which have so many symmetries that they are exactly solvable. Such models have the exciting possibility to be understood in all aspects and thus give valuable insights into physical phenomena. In this way, integrable models offer a unique approach to tackling open problems in physics, such as, for instance, describing strongly coupled systems.

Objective

The aim of this proposal is to develop a new method to find and classify new integrable systems. Our approach is based on a new framework which was very recently put forward by the PI and his group. This new approach was applied to models that are closely related to regular integrable systems from string theory, quantum field theory, and condensed matter physics. Several new models were discovered in this way, but their physical and mathematical properties still remain to be understood.

Focus on Long-Range Interactions

FAIM will be particularly focused on models that have long-range interactions. These models are crucial in understanding strong coupling behavior in, for instance, integrable models that appear in the AdS/CFT correspondence. Understanding long-range interactions is paramount to the computation of correlation functions in these models. Long-range interactions are also important for quantum systems in condensed matter, such as cellular automatons.

Broader Implications

More generally, integrable structures appear in basically all areas of physics. For this reason, finding new integrable models and classifying them will have a large multidisciplinary impact, with exciting applications ranging from condensed matter to string theory. This will potentially help us understand physical phenomena in various different fields.