The electromagnetic duality and the 3+1D O(6) non-linear sigma model with a level-1 Wess-Zumino-Witten term

TL;DR

This paper demonstrates electromagnetic duality in a (3+1)D O(6) non-linear sigma model with a level-1 Wess-Zumino-Witten term, revealing dual phases, monopole-charge exchange, and potential self-dual critical points.

Contribution

It introduces a novel duality framework for the (3+1)D O(6) sigma model with a Wess-Zumino-Witten term, extending concepts of deconfined quantum criticality to higher dimensions.

Findings

Duality exchanges monopoles and charges in the model.

Condensation of monopoles can induce a Neel to VBS phase transition.

Existence of two fractionalized phases with gapless gauge bosons.

Abstract

We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 Wess-Zumino-Witten term, exhibits the electromagnetic duality. If we name the six components of the sigma field as the Neel and valence-bond-solid (VBS) order parameters, the hedgehogs of the Neel and VBS order play the role of monopole and charge. The duality corresponds to the exchange of monopole and charge hence the exchange of the Neel and VBS order. The condensation of monopole can trigger a direct Neel $\leftrightarrow$ VBS phase transition. We conjecture that the critical point is self-dual, which is a generalization of the deconfined quantum critical point in (2+1)-D. In this theory, there exist two deconfined phases where the Neel/VBS hedgehogs are massive but cost finite energy. This leads to two fractionalized phases with particles carrying fractional spin or VBS quantum numbers and gapless gauge bosons.