$(k,n)$-fractonic Maxwell theory

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, $\dots$) 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 $\omega \sim q^n$.

6 pages, 1 figure

References in corpus (5)

• Local stabilizer codes in three dimensions without string logical operators
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Lattice Gerbe Theory
• ${\mathbb{Z}}_2$ Lattice Gerbe Theory