Emergent higher-symmetry protected topological orders in the confined phase of $U(1)$ gauge theory

Salvatore D. Pace, Xiao-Gang Wen

We consider compact $U^{\kappa }(1)$ gauge theory in 3+1D with the $2\pi$-quantized topological term ${\sum }_{I,J=1}^{\kappa }\frac{K_{IJ}}{4\pi }{\int }_{M^4}{F}^I\wedge F^J$. At energies below the gauge…