Fractonic order in infinite-component Chern-Simons gauge theories

2+1D multi-component $U(1)$ gauge theories with a Chern-Simons (CS) term provide simple and complete characterization of Abelian topological orders. In this paper, we extend the theory by taking number component fields to infinity find that they can describe interesting types 3+1D "fractonic" order. "Fractonic" describes peculiar phenomena point excitations in certain strongly interacting systems either cannot move at all or are only allowed lower dimensional sub-manifold. simplest cases infinite-component CS theory, different components do not couple each other decoupled stack fractional Quantum Hall quasi-particles moving 2D planes -- hence fractonic system. We when through term, more varieties orders possible. For example, may foliated for which increasing system size requires insertion nontrivial states. Moreover, examples lie beyond foliation framework, characterized infinite order braiding statistics strictly local.