Abstract

Statistical field theory has played a foundational role in the development of modern non-perturbative methods in theoretical physics, with quantum field theory at its core. Over the years, a wide range of approaches, originating from different areas of physics and mathematics, have been developed and successfully applied to problems in statistical mechanics and condensed matter physics, often yielding quantitative predictions that have subsequently been experimentally confirmed. Concepts such as the S-matrix, bootstrap methods, universality, the operator product expansion, dualities, exact solvability, and, more recently, entanglement-based probes, protected observables, and generalised symmetries have profoundly shaped our understanding of quantum field theory, strongly coupled systems, and non-perturbative phenomena. Underlying many of these developments is the study of gauge dynamics and the emergence of collective behaviour across widely different physical settings. Recent advances in conformal field theory, integrable models, quantum information, variational methods, and quantum computation have further broadened the scope of this endeavour. This project addresses a number of central questions in contemporary quantum and statistical field theory using exact, non-perturbative methods. The proposed research activities are organised around five closely connected themes.

(1) Conformal invariance, conformal bootstrap, and universality, with particular emphasis on exact constraints, renormalisation-group fixed points, defect and thermal observables, and critical phenomena in pure and disordered strongly interacting systems.

(2) Topological phases of matter, gauge theories, and generalised symmetries, including anomaly-related phenomena, effective field-theory descriptions, dualities, bosonisation, extended observables, and confinement mechanisms.

(3) Entanglement and quantum information as probes of quantum field theory and many-body dynamics, encompassing mixed-state entanglement, symmetry-resolved observables, entanglement asymmetry, dissipative processes, and quantum-computing and quantum-simulation protocols.

(4) Low-dimensional quantum field theories, integrable models, and solvable deformations, with particular attention to integrability breaking, confinement phenomena, exact spectra, renormalisation-group flows, generalised thermal structures, and complex quantum dynamics.

(5) Quantum field theories out of equilibrium, focusing on thermalisation, transport, generalised hydrodynamics, dissipation, information spreading, and correlation dynamics in interacting quantum systems.

Keywords related to the topic of the proposal: