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

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.

31 pages, version published in JHEP

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• Emergent fracton strings from covariant bi-form gauge field theory