Anisotropic heavy quark potential in strongly-coupled $\mathcal{N}=4$ SYM in a magnetic field

Abstract

In this work we use the gauge/gravity duality to study the anisotropy in the heavy quark potential in strongly coupled $\mathcal{N}=4$ Super-Yang Mills (SYM) theory (both at zero and nonzero temperature) induced by a constant and uniform magnetic field $\mathcal{B}$. At zero temperature, the inclusion of the magnetic field decreases the attractive force between heavy quarks with respect to its $\mathcal{B}=0$ value and the force associated with the parallel potential is the least attractive force. We find that the same occurs at nonzero temperature and, thus, at least in the case of strongly coupled $\mathcal{N}=4$ SYM, the presence of a magnetic field generally weakens the interaction between heavy quarks in the plasma.