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

TL;DR

This paper explores electric-magnetic duality in symmetric tensor gauge theories, revealing its restriction to four dimensions, the role of complex tensor fields in higher dimensions, and the implications for immobile $p$-branes and self-duality conditions.

Contribution

It demonstrates that duality in symmetric tensor gauge theories is dimension-dependent and introduces a hierarchy of higher-rank gauge fields using bi-form calculus.

Findings

Duality holds only in four-dimensional spacetime.

Higher dimensions require complex tensor fields for duality.

Self-duality conditions emerge as BPS equations in 4D Euclidean space.

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 $\partial_{\mu} \partial_{\nu} J^{\mu \nu} = 0$ 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.