Holographic View of Causality and Locality via Branes in AdS/CFT Correspondence

TL;DR

This paper explores how causality and locality in a 5D anti-de Sitter spacetime are reflected in 4D super Yang-Mills theory through holography, emphasizing the role of an infinite operator tower and matching dynamical time-delays.

Contribution

It demonstrates that causality and locality are encoded in super Yang-Mills theory when an infinite tower of operators is included, and it shows precise agreement of dynamical processes between gravity and gauge theory.

Findings

Causality and locality are encoded in super Yang-Mills with an infinite operator tower.

Massive W-bosons and monopoles behave as extended bilocal objects.

Excellent agreement of causal time-delay between AdS supergravity and super Yang-Mills theory.

Abstract

We study dynamical aspects of holographic correspondence between d=5 anti-de Sitter supergravity and $d=4$ super Yang-Mills theory. We probe causality and locality of ambient spacetime from super Yang-Mills theory by studying transmission of low-energy brane waves via an open string stretched between two D3-branes in Coulomb branch. By analyzing two relevant physical threshold scales, we find that causality and locality is encoded in the super Yang-Mills theory provided infinite tower of long supermultiplet operators are added. Massive W-boson and dual magnetic monopole behave more properly as extended, bilocal objects. We also study causal time-delay of low-energy excitation on heavy quark or meson and find an excellent agreement between anti-de Sitter supergravity and super Yang-Mills theory descriptions. We observe that strong `t Hooft coupling dynamics and holographic scale-size relation thereof play a crucial role to the agreement of dynamical processes.