Meson potential energy in a non-conformal holographic model

Abstract

We study the meson potential energy in a non-conformal model at both zero and finite temperature via gauge/gravity duality. This model consists of five-dimensional Einstein gravity coupled to a scalar field with a non-trivial potential. Interestingly, at both zero and finite temperature we find that the relative meson potential energy can be considered as a measure of non-conformality of the theory. At zero temperature we show that parameters of the Cornell potential, i.e. Coulomb strength parameter κ and constant C depends on the energy scale Λ that breaks conformal symmetry and the difference between the number of degrees of freedom of UV and IR fixed points ΔN while QCD string tension σs just depends on the Λ. At finite temperature we see that there is a melting length lmℓ where beyond that the meson dissociates in the plasma and by increasing Λ the value of lmℓ increases while its value decreases by increasing the temperature.