Quantum field theory (QFT) is a universal language of modern theoretical physics. Originally developed to describe the interaction of light and matter, QFT has since found broad and fruitful applications in high energy particle physics, condensed matter, and statistical physics, as well as in cosmology and string theory.

Some of the most deep open problems about the physics of QFTs at strong coupling, which lies beyond the reach of conventional techniques ¿ are newly accessible thanks to recent developments in topological quantum field theory (TQFT). This insight comes with a dramatic evolution of the notion of symmetries in QFT: symmetries can be characterized via topological defects of various dimensions whose multidimensional fusion generalizes wildly the notion of groups to what are called categorical symmetries.

Research Proposal

This research proposal is devoted to the exploration of aspects of these symmetries and their physical applications. Many deep questions on generalized global symmetries remain open: What is the most general structure of symmetries of quantum systems? Can anomalies for such symmetries be classified? What physical infrared (IR) phases saturate those anomalies? Can IR phases be classified based on spontaneous breaking patterns for generalized global symmetries (extending Landau¿s paradigm)? The history of theoretical physics demonstrates that novel insights on symmetries can have a transformative impact on our understanding of nature. This makes the study of generalized global symmetries a very exciting avenue for investigation.

Main Objectives

1. Explore the structure and dynamical consequences of global symmetries and categorical symmetries in QFT and string theory
2. Obtain results that foster interdisciplinary interactions across high-energy physics (HEP), condensed matter physics (CM), quantum gravity (QG) and mathematics (Math)