Effect of orbital currents on the restricted optical sum rule

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We 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-Tc cuprates above the critical temperature Tc. We extend our results to the superconducting state, and comment on the differences and analogies between these two symmetry-breaking phenomena.