Gapless Infinite-component Chern-Simons-Maxwell Theories

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.