  We derive an effective field theory for a type-II fracton starting from the
Haah code on the lattice. The effective topological theory is not given
exclusively in terms of an action; it must be supplemented with a condition
that selects physical states. Without the constraint, the action only describes
a type-I fracton. The constraint emerges from a condition that cube operators
multiply to the identity, and it cannot be consistently implemented in the
continuum theory at the operator level, but only in a weaker form, in terms of
matrix elements of physical states. Informed by these studies and starting from
the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory
that does not need a constraint or projector, and yet has no mobile
excitations. Whether this continuum theory admits a lattice counterpart remains
unanswered.

Strongly Correlated Electrons;High Energy Physics - Theory