Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes

TL;DR

The paper analyzes electric-magnetic duality in Lorentz-invariant symmetric tensor gauge theories that realize fracton physics, showing that a clean duality exists only in $D=4$ with symmetric fields. In dimensions $D>4$, dual descriptions require mixed-symmetry tensor fields, organized via a bi-form calculus that reveals a hierarchical multi-Maxwell structure. The authors demonstrate explicit dualities in $D=5$ (rank-2 symmetric dual to a type $(2,1)$ field) and in $D\ge6$ (dual to type $(D-3,1)$, and more generally $(D-3,k-1)$ for rank-$k$), and they discuss couplings to $p$-brane currents that imply immobility through dipole/multipole conservation. They also derive self-duality (BPS) conditions in Euclidean 4d that involve a traceless constraint, highlighting non-topological bounds and the rich landscape of dual descriptions for fracton-containing theories.

Abstract

We study electric-magnetic duality in Lorentz invariant symmetric tensor gauge theories, where immobile charged particles - fractons - arise due to the generalized current conservation $\partial_μ \partial_ν J^{μν} = 0$ and the fracton gauge principle. We show that the duality in the symmetric gauge theories holds only in four-dimensional spacetime. In higher dimensions, the duality does not hold with only the symmetric gauge fields but tensor fields with more complex symmetries come into play. Furthermore, we show that a hierarchy for the symmetric gauge field theories of higher ranks is interpreted by the bi-form calculus. We also discuss the restricted immobility of $p$-branes in the mixed symmetric gauge theories. As a byproduct, we find that novel self-duality conditions are defined as BPS equations in the four-dimensional Euclidean space.