Time dependent correlators of holographic EPR pairs

We study the field correlators between the quark and anti-quark EPR pair in the super YangMills theory using the holographic description, which is a string in AdS space with its two ends anchored on the boundary. We consider the cases that the end points of the string are static, and that end points are uniformly accelerated in opposite direction where the exact solutions for the string’s profiles are available. In both cases, the two-points correlators of the boundary fields which are described by the linearized perturbations in the worldsheet can also be derived exactly and the all-time evolution of the correlators are obtained. In the case of the accelerating string, the induced geometry on the string worldsheet has the causal structure of a two-sided AdS black hole with a wormhole connects two causally disconnected boundaries, which is a realization of the ER=EPR conjecture. We find that the causality plays an crucial role in determining the nature of the dispersion relation of the particles anchoring at the end points of the string, and the feature of the induced mutual interaction between two particles. In the case of the causally disconnected two ends, the induced effect from the field gives the dissipative dynamics of each particles with no dependence of the distance between two ends, and the induced mutual coupling between two particles vanishes in the late times, following a power law. When two ends are causally connected, the induced dispersion relation becomes non-dissipative at the late times. Here we will also comment on the implication of our findings in the entangled particle dynamics and the ER=EPR conjecture.