Large Quantum Numbers and Long Strings in Conformal and Confining QFTs

This award funds the research activities of Professor Alexander Monin at the University of South Carolina. Quantum field theory provides the basic framework for describing fundamental particles and their interactions, as well as a wide range of phenomena in condensed matter and statistical physics. However, many quantum field theories become difficult to study when interactions are strong and conventional approximation methods no longer apply. Under this award, Professor Monin will investigate how sectors characterized by large quantum numbers can provide new ways to understand such strongly interacting systems. The research will focus on theories with large conserved charges and on systems with large angular momentum, where complex quantum dynamics can often be reorganized into controlled and predictive descriptions. By developing analytic methods for studying strongly coupled quantum systems, this research advances the national interest by promoting the progress of fundamental science and strengthening the theoretical foundations needed to understand physical phenomena across a broad range of scales. The project will also contribute to the training of a graduate student in modern methods of theoretical physics and will support the dissemination of research results through publications, scientific meetings, and educational activities. More technically, Professor Monin will develop complementary approaches to non-perturbative quantum field theory based on large charge and large spin. In conformal field theory, the research will combine large-charge effective field theory with bootstrap methods to study spectra and correlation functions in sectors of fixed large charge, with particular emphasis on extending heavy-light bootstrap methods beyond scalar probes and clarifying the relation between crossing-symmetric solutions and their effective-field-theory realizations. Related controlled limits will be used to test and refine these large-charge descriptions. In confining theories, Professor Monin will use effective string theory to investigate large-spin states, including extensions from rotating open strings to folded closed strings and string-junction configurations relevant to hadronic systems. The project will seek universal predictions that can be compared with perturbative, bootstrap, and lattice results, thereby improving analytic control over strongly coupled quantum field theories in regimes where conventional perturbation theory is insufficient. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.