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We study the correlators of the fields that couple to the quark andanti-quark EPR pair in the super Yang-Mills theory using the holographicdescription, which is a string in AdS space with its two ends anchoring on theboundaries. We consider the cases that the endpoints of the string are staticand that the endpoints are uniformly accelerated in opposite directions wherethe exact solutions for the string's profiles are available. In both cases, thetwo-point correlators of the boundary field, described by the linearizedperturbations in the worldsheet, can also be derived exactly where we obtainthe all-time evolution of the correlators. In the case of the acceleratingstring, the induced geometry on the string worldsheet has the causal structureof a two-sided AdS black hole with a wormhole connecting two causallydisconnected boundaries, which can be a realization of the ER=EPR conjecture.We find that causality plays a crucial role in determining the nature of thedispersion relation of the particle and the feature of the induced mutualinteraction between two particles from the field. In the case that twoboundaries of the worldsheet are causally disconnected, the induced effect fromthe field gives the dissipative dynamics of each particle with no dependence onthe distance between two particles, and the induced mutual coupling betweenthem vanishes in the late times, following a power law. When two ends arecausally connected, the induced dispersion relation becomes non-dissipative inthe late times. Here, we will also comment on the implications of our findingsto the entangled particle dynamics and the ER=EPR conjecture.

Time dependent field correlators from holographic EPR pairs