Solving Field Theory with Integrability

• Applicant: Dr. Till Bargheer
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 460391856

Quantum field theory (QFT) is arguably the most important framework of theoretical physics, describing a broad range of phenomena across a large range of scales. In particular, the extremely successful Standard Model of particle physics is formulated in terms of gauge theory. At the same time, our analytical access to QFT is largely limited to perturbation theory, which only applies at weak coupling, and quickly becomes intractable.The goal of this project is a comprehensive study of quantum field theory with the help of integrability. Integrable models are characterized by an extended spectrum of symmetries. These give rise to advanced solution techniques that admit exact, non-perturbative descriptions of physical observables. Integrability hence provides the opportunity to study aspects of QFT that are in most cases inaccessible by any other means. A central player in this project is N=4 super Yang-Mills theory (SYM), which takes a special role in the space of quantum field theories. Via the AdS/CFT correspondence, the theory is dual to a higher-dimensional string theory, which yields an entirely new window to strongly-coupled gauge theory. Conversely,weakly-coupled gauge theory describes quantum strings, and therefore provides insights into a consistent theory of quantum gravity. Moreover,due to its enhanced symmetry, the theory has been fundamental for many of the modern developments in the field of scattering amplitudes and correlation functions.The enlarged symmetry of this theory becomes even more pronounced in the planar limit of a large gauge group, where it extends to integrability. Based on this integrability, powerful descriptions of the planar spectrum and scattering amplitudes have been found in recent years. Work by a group including the applicant has shown that the integrability even applies beyond the planar limit. The integrable structure provides a chance to exactly solve an interacting four-dimensional quantum gauge theory for the first time in history.This project aims at developing and applying integrability techniques to determine exact, non-perturbative descriptions for the correlation functions of this theory, and to extract lessons for more general theories. It is directed towards the ultimate goal of completely solving the theory, which will significantly enhance our understanding of quantum field theory in general, and have applications to more realistic theories.

• DFG Programme: Independent Junior Research Groups