Yangian Symmetry in Quantum Gauge Field Theory

• Applicant: Professor Dr. Jan Plefka
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2016 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 324161040

Our understanding of nature at its deepest level is governed by symmetries. This proposal aims at studying hidden symmetries in quantum field theory going beyond the established space-time symmetries of the Poincare group and its supersymmetric or conformal extensions. Our approach is divided into three research strands. They are grounded on our discovery of an infinite dimensional symmetry for the S-matrix of maximally supersymmetric gauge theory in four dimensions, known as the Yangian. In the first strand we will investigate the implication of the hidden symmetry for smooth Wilson loop observables, providing novel tools for exact, non-perturbative results. In the second strand we will study the Yangian symmetry as a classical symmetry of the action rather than as a dynamical symmetry of quantum observables. This aims at a classification of Yangian symmetric quantum field theories in four dimensions and is expected to constrain the quantum effective action. Finally, we shall analyze Yangian symmetry in 4D quantum field theory from the viewpoint of a generalized Haag-Lopuszanski-Sohnius theorem upon allowing for a non-trivial co-product. The ultimate goal of these research strands is to innovate the standard perturbative approach in quantum field theory by expanding in perturbations about an integrable model, such as N=4 gauge theory.

• DFG Programme: Research Grants