  A powerful mechanism for constructing gauge theories is to start from a
theory with a global symmetry, then apply the "gauge principle," which demands
that this symmetry hold locally. For example, the global phase rotation of a
system of conserved charges can be promoted to a local phase rotation by
coupling to an ordinary U(1) vector gauge field. More recently, a class of
particles has been studied featuring not only charge conservation, but also
conservation of higher moments, such as dipole moment, which leads to severe
restrictions on the mobility of charges. These particles, called fractons, are
known to be intimately connected to symmetric tensor gauge fields. In this
work, we show how to derive such tensor gauge theories by applying the gauge
principle to a theory of ungauged fractons. We begin by formulating a field
theory for ungauged fractons exhibiting global conservation of charge and
dipole moment. We show that such fracton field theories have a characteristic
non-Gaussian form, reflecting the fact that fractons intrinsically interact
with each other even in the absence of a mediating gauge field. We then promote
the global higher moment conservation laws to local ones, which requires the
introduction of a symmetric tensor gauge field. Finally, we extend these
arguments to other types of subdimensional particles besides fractons. This
work offers a possible route to the formulation of non-abelian fracton
theories.
