Chern-Simons Theory and Fracton

Fracton order describes the peculiar phenomena that point excitations in certain strongly interacting systems either cannot move at all or are only allowed to move in a lower dimensional sub-manifold. It has recently been discovered in various lattice models, tensor gauge theories, etc. In this talk, I will discuss how the 2+1D Chern-Simons (CS) gauge theory can be used to provide new insights and explore new possibilities in 3+1D fracton order. 2+1D U(1) gauge theories with a CS term provide a simple and complete characterization of 2+1D Abelian topological orders. To study 3+1D fracton order, we extend the theory by taking the number of component gauge fields to be infinity. In the simplest case of infinite-component CS gauge theory, different components do not couple to each other and the theory describes a decoupled stack of 2+1D fractional Quantum Hall systems with quasi-particles moving only in 2D planes -- hence a fractonic system. More interestingly, we find that when the component gauge fields do couple through the CS term, more varieties of fractonic orders are possible. For example, they may describe foliated fractonic systems which extends the framework found in exactly solvable models. At the same time, we find examples which lie beyond the foliation framework, characterized by 2D excitations of infinite order and braiding statistics that are not strictly local.

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