2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/21402We derive the restricted optical-conductivity sum rule for a model with circulating orbital currents. It is shown that an unusual coupling of the vector potential to the interaction term of the model Hamiltonian results in a non-standard form of the sum rule. As a consequence, the temperature dependence of the restricted spectral weight could be compatible with existing experimental data for high-$T_c$ cuprates above the critical temperature $T_c$. We extend our results to the superconducting state, and comment on the differences and analogies between these two symmetry-breaking phenomena.Revised version, to appear in EPJBStrongly Correlated ElectronsSuperconductivitytext