Holographic imaginary potential of a quark antiquark pair in the presence of gluon condensation

Abstract

For a moving heavy quark antiquark (QQ) in a quark gluon plasma (QGP), we use gauge/gravity duality to study both real and imaginary parts of the potential ($$ \operatorname{Re}{V}_{Q\overline{Q}} $$ Re V Q Q ¯ and $$ \operatorname{Im}{V}_{Q\overline{Q}} $$ Im V Q Q ¯ respectively) in a gluon condensate (GC) theory. The complex potential is derived from the Wilson loop by considering the thermal fluctuations of the worldsheet of the Nambu-Goto holographic string. We calculate $$ \operatorname{Re}{V}_{Q\overline{Q}} $$ Re V Q Q ¯ and $$ \operatorname{Im}{V}_{Q\overline{Q}} $$ Im V Q Q ¯ in both cases where the axis of the moving $$ Q\overline{Q} $$ Q Q ¯ pair is transverse and parallel with respect to its direction of movement in the plasma. Using the renormalization scheme for the $$ \operatorname{Re}{V}_{Q\overline{Q}} $$ Re V Q Q ¯ , we find that the inclusion of GC increases the dissociation length while rapidity has the opposite effect. While for the $$ \operatorname{Im}{V}_{Q\overline{Q}} $$ Im V Q Q ¯ , we observe that by considering the effect of GC, the $$ \operatorname{Im}{V}_{Q\overline{Q}} $$ Im V Q Q ¯ is generated for larger distance thus decreasing quarkonium dissociation, while rapidity has opposite effect. In particular, as the value of GC decreases in the deconfined phase, the $$ \operatorname{Im}{V}_{Q\overline{Q}} $$ Im V Q Q ¯ is generated for smaller distance thus enhancing quarkonium dissociation, and at high temperatures it is nearly not modified by GC, consistent with previous findings of the entropic force.