Time dependent field correlators from holographic EPR pairs

TL;DR

This paper investigates time-dependent field correlators in holographic EPR pairs within super Yang-Mills theory, revealing how causality influences particle interactions and supporting the ER=EPR conjecture through exact solutions in AdS space.

Contribution

It provides exact solutions for field correlators in static and accelerated EPR pairs, demonstrating the role of causality and the induced geometry on particle dynamics in holography.

Findings

Causality determines the nature of particle dispersion relations.

Induced mutual interactions vanish at late times when boundaries are causally disconnected.

The geometry of the string worldsheet reflects ER=EPR through a wormhole structure.

Abstract

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.