Holographic Schwinger-Keldysh effective action for heavy quarks in confinement and deconfinement phases

The holographic Schwinger-Keldysh (SK) prescription proposed by Skenderis and van Rees (SvR) has the advantage of being applicable whether or not the gravity dual contains a black hole. Taking advantage of this feature, we derive the quadratic effective action for a quark-antiquark pair in the confinement phase within the holographic SK framework of SvR. We also apply the SvR prescription to derive the quadratic effective action for a single heavy quark moving at a constant velocity in a nonequilibrium steady state in the deconfinement phase.