Quantum Field Theory, Exotic Symmetries, and Fractons

Abstract

Quantum field theory has been extremely successful in organizing and classifying phases of matter and transitions between them. However, physicists have recently discovered a new class of phases, dubbed fracton phases, which do not admit a standard continuum quantum field theory description. One has to extend the framework of quantum field theory to incorporate these phases. In this thesis, I investigate various aspects of quantum field theories with exotic global symmetries, or exotic QFTs, that capture the low-energy physics of fractons and other exotic lattice models. In chapter 2, I introduce a Euclidean spacetime lattice formulation for discretizing a continuum quantum field theory on a lattice while retaining its nice features, such as symmetries, anomalies, dualities, etc. It provides a rigorous framework for analyzing exotic QFTs by regularizing various singularities and infinities. This content is based on work with Ho Tat Lam, Nathan Seiberg, and Shu-Heng Shao [1]. In chapters 3 and 4, I use the above formulation to construct new gapless and gapped exotic lattice models, including fracton models. The novel feature of these models is that they can be defined on an arbitrary spatial graph, as opposed to a regular lattice. I also find intriguing connections between observables in these models and certain algebraic quantities associated with the graph. For instance, the ground state degeneracy of one of the models is the number of spanning trees of the graph, a fundamental measure of complexity of the graph. This content is based on works with Ho Tat Lam, Nathan Seiberg, and Shu-Heng Shao [2,3].