Fractonic order in infinite-component Chern-Simons gauge theories

TL;DR

This paper explores how infinite-component Chern-Simons gauge theories can model various types of 3+1D fractonic orders, revealing new phenomena and extending the understanding of topological phases.

Contribution

It introduces the extension of multi-component U(1) gauge theories to infinite components, describing novel fractonic orders including foliated and non-foliated types.

Findings

Decoupled components model 2+1D fractional Quantum Hall systems with restricted particle motion.

Coupled components lead to diverse fractonic orders, including foliated and non-foliated types.

Examples include systems with nonlocal braiding statistics and infinite-order excitations.

Abstract

2+1D multi-component $U(1)$ gauge theories with a Chern-Simons (CS) term provide a simple and complete characterization of 2+1D Abelian topological orders. In this paper, we extend the theory by taking the number of component gauge fields to infinity and find that they can describe interesting types of 3+1D "fractonic" order. "Fractonic" 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. In the simplest cases 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. 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 for which increasing the system size requires insertion of nontrivial 2+1D topological states. Moreover, we find examples which lie beyond the foliation framework, characterized by 2D excitations of infinite order and braiding statistics that are not strictly local.