  The scope of quantum field theory is extended by introducing a broader class
of discrete gauge theories with fracton behavior in 2+1D. We consider
translation invariant systems that carry special charge conservation laws,
which we refer to as exponential polynomial symmetries. Upon gauging these
symmetries, the resulting $\mathbb{Z}_N$ gauge theories exhibit fractonic
physics, including constrained mobility of quasiparticles and UV dependence of
the ground state degeneracy. For appropriate values of theory parameters, we
find a family of models whose excitations, albeit being deconfined, can only
move in the form of bound states rather than isolated monopoles. For
concreteness, we study in detail the low-energy physics and topological sectors
of a particular model through a universal protocol, developed for determining
the holonomies of a given theory. We find that a single excitation, isolated in
a region of characteristic size $R$, can only move from its original position
through the action of operators with support on $\mathcal{O}(R)$ sites.
Furthermore, we propose a Chern-Simons variant of these gauge theories,
yielding non-CSS type stabilizer codes, and propose the exploration of
exponentially symmetric subsystem SPTs and fracton codes in 3+1D.
