$(k,n)$-fractonic Maxwell theory

TL;DR

This paper introduces a generalized class of fractonic Maxwell theories, called (k,n)-fractonic Maxwell theory, which extends mobility restrictions to higher multipoles and tensorial charges, revealing new photonic excitations with dispersion relations depending on n.

Contribution

It generalizes fractonic U(1) gauge theories to (k,n)-fractonic Maxwell theories using symmetric tensors, expanding the types of charges and excitations considered.

Findings

Higher order multipole mobility restrictions introduced.

Tensorial densities characterize fractonic charges.

Photonic excitations exhibit dispersion f f q^n.

Abstract

Fractons emerge as charges with reduced mobility in a new class of gauge theories. Here, we generalise fractonic theories of $U(1)$ type to what we call $(k,n)$-fractonic Maxwell theory, which employs symmetric order-$n$ tensors of $k$-forms (rank-$k$ antisymmetric tensors) as "vector potentials". The generalisation has two key manifestations. First, the objects with mobility restrictions extend beyond simple charges to higher order multipoles (dipoles, quadrupoles, $\ldots$) all the way to $n^\mathrm{th}$-order multipoles. Second, these fractonic charges themselves are characterized by tensorial densities of $(k-1)$-dimensional extended objects. The source-free sector exhibits `photonic' excitations with dispersion $\omega\sim q^n$.