  We study the correlators of the fields that couple to the quark and
anti-quark EPR pair in the super Yang-Mills theory using the holographic
description, which is a string in AdS space with its two ends anchoring on the
boundaries. We consider the cases that the endpoints of the string are static
and that the endpoints are uniformly accelerated in opposite directions where
the exact solutions for the string's profiles are available. In both cases, the
two-point correlators of the boundary field, described by the linearized
perturbations in the worldsheet, can also be derived exactly where we obtain
the all-time evolution of the correlators. 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 connecting two causally
disconnected boundaries, which can be a realization of the ER=EPR conjecture.
We find that causality plays a crucial role in determining the nature of the
dispersion relation of the particle and the feature of the induced mutual
interaction between two particles from the field. In the case that two
boundaries of the worldsheet are causally disconnected, the induced effect from
the field gives the dissipative dynamics of each particle with no dependence on
the distance between two particles, and the induced mutual coupling between
them vanishes in the late times, following a power law. When two ends are
causally connected, the induced dispersion relation becomes non-dissipative in
the late times. Here, we will also comment on the implications of our findings
to the entangled particle dynamics and the ER=EPR conjecture.
