Covariant interacting fractons

We show that there exists a natural analog of the Yang-Mills equations using the Frölicher-Nijenhuis bracket between vector-valued differential forms. The gauge field is a rank-2 tensor, and when one constrains it to be symmetric, then the system exhibits fractonic behaviors. In the linearized limit, the constrained equations of motion reduce to those of the covariant fracton model [., ., and Notes from the bulk, Ph.D. thesis, Università di Genova, 2024.].