Heavy quark potential with hyperscaling violation

In this paper, we investigate the behavior of the heavy quark potential in the backgrounds with hyperscaling violation. The metrics are covariant under a generalized Lifshitz scaling symmetry with the dynamical Lifshitz parameter $z$ and hyperscaling violation exponent $\theta$. We calculate the potential for a certain range of $z$ and $\theta$ and discuss how it changes in the presence of the two parameters. Moreover, we add a constant electric field to the backgrounds and study its effects on the potential. It is shown that the heavy quark potential depends on the non-relativistic parameters. Also, the presence of the constant electric field tends to increase the potential.