Gapless Infinite-component Chern-Simons-Maxwell Theories

TL;DR

This paper explores the unique properties of gapless infinite-component Chern-Simons-Maxwell theories in 3+1D, revealing their robustness, deconfined nature, and topological features, with a new continuous field theory description.

Contribution

It demonstrates that gapless iCSM theories are deconfined and robust, unlike 2+1D Maxwell theories, and introduces a continuous field theory capturing their topological and symmetry-breaking features.

Findings

Gapless iCSM theories are deconfined and robust against local perturbations.

Spontaneous breaking of an exotic one-form symmetry explains gaplessness.

A continuous field theory captures the topological features of certain iCSM models.

Abstract

The infinite-component Chern-Simons-Maxwell (iCSM) theory is a 3+1D generalization of the 2+1D Chern-Simons-Maxwell theory by including an infinite number of coupled gauge fields. It can be used to describe interesting 3+1D systems. In Phys. Rev. B 105, 195124 (2022), it was used to construct gapped fracton models both within and beyond the foliation framework. In this paper, we study the nontrivial features of gapless iCSM theories. In particular, we find that while gapless 2+1D Maxwell theories are confined and not robust due to monopole effect, gapless iCSM theories are deconfined and robust against all local perturbation and hence represent a robust 3+1D deconfined gapless order. The gaplessness of the gapless iCSM theory can be understood as a consequence of the spontaneous breaking of an exotic one-form symmetry. Moreover, for a subclass of the gapless iCSM theories, we find interesting topological features in the correlation and response of the system. Finally, for this subclass of theories, we propose a fully continuous field theory description of the model that captures all these features.