Abstract

Quantum field theory (QFT) is the fundamental language with which physics describes nature, from interactions between elementary particles to the collective phenomena of condensed matter and statistical mechanics. However, many of the theories most relevant to describing the physical world are strongly coupled and cannot be studied using traditional methods, such as perturbation theory. Understanding them requires a rethinking of the conceptual structures underlying QFT and, at the same time, new analytical and numerical tools.

The QFTLand project, funded by the Italian Science Fund (FIS) of the Ministry of Education, Universities and Research (MUR), tackles this challenge in three directions. The first concerns symmetries: in recent years, it has become apparent that the classical notion of symmetry based on groups is incomplete and that ‘generalised’ symmetries exist, such as non-invertible ones. The project will study an even more general class of structures—quantum groups—which act as symmetries in two-dimensional conformal theories, in order to identify the most general form of symmetry that a QFT can possess. The second area focuses on extended operators (lines, surfaces), which implement symmetries and play a role in diffusion processes between particles, with the aim of clarifying their role in open problems such as fermion-monopole scattering. The third research area goes beyond unitaryity: many statistical mechanics systems, such as percolation, are described by non-unitary theories, for which the project will develop fractional-dimensional expansions and numerical methods inspired by the conformal bootstrap.

QFTLand thus aims to broaden the landscape of known field theories and to provide new tools for tackling open problems in high-energy physics, condensed matter physics and statistical mechanics.