Emergent fracton strings from covariant bi-form gauge field theory

A bstract We present a covariant field-theoretical framework for a rank-4 tensor gauge field theory describing fractonic string-like objects. We show that the most general quadratic, parity-preserving action naturally leads to a Maxwell-like sector, with tensorial analogues of electric and magnetic fields, Maxwell-like equations, energy-momentum tensor, and a Lorentz-like force. Remarkably, the theory gives rise to fracton-like string excitations purely from symmetry principles: constraints on the motion of these extended objects appear as Gauss-like laws, without being imposed by hand. One of these laws is new and corresponds to a generalised dipole conservation for closed strings, restricting their mobility and defining a novel class of fractonic string-like excitations. Finally, we uncover a connection to linearised area-metric gravity: in a suitable limit, the theory reduces to known covariant fracton models with rank-2 gauge fields, highlighting a deep link between fractonic matter and gravity-like structures. This provides a unified perspective on higher-rank gauge fields, extended excitations, and emergent gravitational features.