  The emerging study of fractons, a new type of quasi-particle with restricted
mobility, has motivated the construction of several classes of interesting
continuum quantum field theories with novel properties. One such class consists
of foliated field theories which, roughly, are built by coupling together
fields supported on the leaves of foliations of spacetime. Another approach,
which we refer to as exotic field theory, focuses on constructing Lagrangians
consistent with special symmetries (like subsystem symmetries) that are
adjacent to fracton physics. A third framework is that of infinite-component
Chern-Simons theories, which attempts to generalize the role of conventional
Chern-Simons theory in describing (2+1)D Abelian topological order to fractonic
order in (3+1)D. The study of these theories is ongoing, and many of their
properties remain to be understood.
  Historically, it has been fruitful to study QFTs by embedding them into
string theory. One way this can be done is via D-branes, extended objects whose
dynamics can, at low energies, be described in terms of conventional quantum
field theory. QFTs that can be realized in this way can then be analyzed using
the rich mathematical and physical structure of string theory. In this paper,
we show that foliated field theories, exotic field theories, and
infinite-component Chern-Simons theories can all be realized on the
world-volumes of branes. We hope that these constructions will ultimately yield
valuable insights into the physics of these interesting field theories.
