Electromagnetic anomaly in the presence of electric and chiral magnetic conductivities in relativistic heavy-ion collisions

We study the spacetime evolution of electric $(\mathbf{\text{E}})$ and magnetic $(\mathbf{\text{B}})$ fields along with the electromagnetic anomaly $(\mathbf{\text{E}}\cdot \mathbf{\text{B}})$ in the presence of electric ($\sigma$) and chiral magnetic (${\sigma }_{\chi }$) conductivities in Au+Au collisions at $\sqrt{s_{\mathrm{N}\mathrm{N}}}=200$~GeV. By comparing to the Lienard-Wiechert solutions with zero conductivities, we observe a symmetry breaking of the electromagnetic field in a conducting medium with respect to the reaction plane. The decay of the field is also significantly decelerated after the conductivities are introduced. Similar effects are also found for the dipole structure of $\mathbf{\text{E}}\cdot \mathbf{\text{B}}$ as well as the quadrupole structure of $(\mathbf{\text{E}}\cdot \mathbf{\text{B}})\mathbf{\text{B}}$, which may finally affect the charge separation of the elliptic flow coefficient of hadrons observed in high-energy nuclear collisions.