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.

21 pages, 10 figures, references are added