  Fracton order is an intriguing new type of order which shares many common
features with topological order, such as topology-dependent ground state
degeneracies, and excitations with mutual statistics. However, it also has
several distinctive geometrical aspects, such as excitations with restricted
mobility, which naturally lead to effective descriptions in terms of higher
rank gauge fields. In this paper, we investigate possible effective field
theories for 3D fracton order, by presenting a general philosophy whereby
topological-like actions for such higher-rank gauge fields can be constructed.
Our approach draws inspiration from Chern-Simons and BF theories in 2+1
dimensions, and imposes constraints binding higher-rank gauge charge to
higher-rank gauge flux. We show that the resulting fractonic Chern-Simons and
BF theories reproduce many of the interesting features of their familiar 2D
cousins. We analyze one example of the resulting fractonic Chern-Simons theory
in detail, and show that upon quantization it realizes a gapped fracton order
with quasiparticle excitations that are mobile only along a sub-set of
1-dimensional lines, and display a form of fractional self-statistics. The
ground state degeneracy of this theory is both topology- and geometry-
dependent, scaling exponentially with the linear system size when the model is
placed on a 3-dimensional torus. By studying the resulting quantum theory on
the lattice, we show that it describes a $\mathbb{Z}_s$ generalization of the
Chamon code.
