3d Quantum Field Theories

In this project, we will perform an analysis of certain types of equivalence relations on the space of three-dimensional (3d) Quantum Field Theories (QFTs) in search of hidden structures and features that organize this space and help classify 3d QFTs. Specifically, we will study the infinite web of dualities that can be constructed from a simple set of path integral operations in certain 3d QFTs, which can be mnemonically realized as graph operations. The graph representation of the data that defines the kinematical structure of these 3d QFTs, and the realization of dualities therein as graph operations, naturally opens the door to their study by use of Machine Learning (ML) techniques, namely Graph Neural Networks (GNN). In short, this project will focus primarily on the use of GNNs, and other concepts in ML broadly defined, as the methodological basis for a novel study of dualities in 3d QFTs. See the lecture notes for some physics background, and this paper} and this for recent works using machine learning to study somewhat similar problems.