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

A bstract We study electric-magnetic duality in Lorentz invariant symmetric tensor gauge theories, where immobile charged particles — fractons — arise due to the generalized current conservation ∂ μ ∂ 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.