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A 3d Boson Topological Insulator and the “Statistical Witten Effect”

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Electron topological insulators are members of a broad class of “symmetry protected topological” (SPT) phases of fermions and bosons which possess distinctive surface behavior protected by bulk symmetries. For 1d and 2d SPT’s the surfaces are either gapless or symmetry broken, while in 3d, gapped symmetry-respecting surfaces with (intrinsic) 2d topological order are also possible. The electromagnetic response of (some) SPT’s can provide an important characterization, as illustrated by the Witten effect in 3d electron topological insulators. Using a 3d parton-gauge theory construction, we have recently developed a dyon condensation approach to access exotic new phases including some 3d bosonic SPT’s. A bosonic SPT with both time-reversal and charge conservation symmetries, is thereby obtained, a phase which supports a gapped, symmetry-unbroken 2d surface with topological order - a toric code with charge one-half anyons. The 3d electromagnetic response of this bosonic SPT phase is quite remarkable - an external magnetic monopole can remain charge neutral, but is statistically transmuted becoming a fermion - a “statistical Witten effect” that characterizes the phase.