Strings as Hyper-Fractons
Erica Bertolini, Hyungrok Kim
TL;DR
The paper addresses how to classify Gauss-law constraints that respect spatial rotation symmetry across dimensions and gauge-field ranks, and how these constraints determine conserved multipole charges. It develops a representation-theoretic framework based on SO$(d)$ to predict conserved moments via the cokernel of a branching map, yielding three mobility regimes: non-fractonic, fractonic, and hyper-fractonic. A key finding is that many higher-form gauge theories, including $p$-form electrodynamics, realize hyper-fractonic behaviour with an infinite tower of conserved moments, forcing motion to couple to extended objects like strings or branes. The work unifies and extends fracton phenomenology, shows extensive low-rank hyper-fractonic occurrences, and provides a roadmap for constructing new hyper-fractonic theories and exploring their relations to higher gauge theories and Ward identities.
Abstract
We systematically examine all possible Gauss laws obeying spatial rotation symmetry, characterising the corresponding conserved charges. In the case of conserved higher moments, this gives rise to fractonic behaviour. We show that many Gauss laws, including those arising from $p$-form electrodynamics, in fact, produce an infinite tower of conserved moments, which we dub hyper-fractonic. In hyper-fractonic systems, a finite number of charged particles cannot be mobile due to an inability of fulfilling the infinite number of conservation laws with a finite number of degrees of freedom. Instead, mobile charged objects must have an infinite number of degrees of freedom. In particular, the strings and branes naturally coupling to $p$-form potentials provide an example of hyper-fractonic matter.