Thermodynamics, imaginary potential, and string breaking of heavy quarkonium in the anisotropic background

We study the thermodynamics of the heavy quarkonium and string breaking in the anisotropic media by gravity/gauge duality. The degree of anisotropy is characterized by the dynamical exponent $\ensuremath{\nu}$, with $\ensuremath{\nu}=1$ representing the isotropic case. The free energy of the heavy quarkonium, which is obtained through the Wilson loop, is investigated in an anisotropic background. It is found that the free energy is suppressed by the dynamical exponent $\ensuremath{\nu}$. The results also show that the anisotropy induced by anisotropic pressure significantly influences the free energy of the Coulombic part, in contrast to the effect of anisotropy induced by the magnetic field. Additionally, we find that when $\ensuremath{\nu}$ increases, both the absolute value of the imaginary potential and the thermal width increase. Finally, the string breaking is investigated in the confinement phase which corresponds to the zero temperature. It is found that the heavy meson is easier to decay in the presence of anisotropy compared to the isotropic case for the decay mode $Q\overline{Q}\ensuremath{\rightarrow}Q\overline{q}+\overline{Q}q$.