Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

$(k,n)$-fractonic Maxwell theory

Vijay B. Shenoy, Roderich Moessner

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 $ω\sim q^n$.

$(k,n)$-fractonic Maxwell theory

Abstract

Fractons emerge as charges with reduced mobility in a new class of gauge theories. Here, we generalise fractonic theories of type to what we call -fractonic Maxwell theory, which employs symmetric order- tensors of -forms (rank- 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, ) all the way to -order multipoles. Second, these fractonic charges themselves are characterized by tensorial densities of -dimensional extended objects. The source-free sector exhibits `photonic' excitations with dispersion .

Paper Structure

This paper contains 1 section, 37 equations, 1 figure.

Table of Contents

  1. (2,2)-fracton theory

Figures (1)

  • Figure 1: Illustration of tensor charge mobility constraint of (2,2)-fracton theory, see appendix. Charges of this theory are 2-nd rank symmetric tensors, represented by an ellipse indicating principal axes. On the top panel the total charge vanishes (red is positive charge, blue is negative charge), but the system has a net dipole moment. A rearrangement of the charges which changes the dipole moment is forbidden (bottom left), while a dipole-preserving "rigid" translations of both charges is allowed (bottom right).