2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/25691We uncover new topology-related features of the $π$-flux saddle-point solution of the $D$=2+1 Heisenberg antiferromagnet. We note that symmetries of the spinons sustain a built-in competition between antiferromagnetic (AF) and valence-bond-solid (VBS) orders, the two tendencies central to recent developments on quantum criticality. An effective theory containing an analogue of the Wess-Zumino-Witten term is derived, which generates quantum phases related to AF monopoles with VBS cores, and reproduces Haldane's hedgehog Berry phases. The theory readily generalizes to $π$-flux states for all $D$.4 pages, revisedStrongly Correlated ElectronsSuperconductivitytext