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

Abstract: For a moving heavy quark antiquark ($Q\bar{Q}$) in a quark gluon plasma (QGP), we use gauge/gravity duality to study both real and imaginary parts of the potential (Re$V_{Q\bar{Q}}$ and Im$V_{Q\bar{Q}}$ 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 Re$V_{Q\bar{Q}}$ and Im$V_{Q\bar{Q}}$ in both cases where the axis of the moving $Q\bar{Q}$ pair is transverse and parallel with respect to its direction of movement in the plasma. Using the renormalization scheme for the Re$V_{Q\bar{Q}}$ , we find that the inclusion of GC increases the dissociation length while rapidity has the opposite effect. While for the Im$V_{Q\bar{Q}}$ , we observe that by considering the effect of GC, the Im$V_{Q\bar{Q}}$ 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 Im$V_{Q\bar{Q}}$ 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.