The fracton gauge principle

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 $U\left(1\right)$ 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.

Figure 1

Theories with only charge conservation have local dipole creation operators, which lead to quadratic terms in the continuum field theory limit. In contrast, a theory with dipole moment conservation has no such dipole creation operators. In this case, the smallest creation operators are quadrupolar, leading to quartic terms in the field theory.

Figure 2

Fractons can interact via the exchange of virtual dipoles, allowing two fractons to “push off” of each other.