Holographic view of causality and locality via branes in AdS/CFT correspondence

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.

Holography of radiation and jet quenching

“…Mikhailov pointed out the ref [14]. where the flight time analysis in the flat boundary case is done.…”

AdS-CFT correspondence and the information paradox

“…On the supergravity side the particles hardly interact at all and move past each other with only a small deflection, but on the gauge theory side the objects completely merge during the collision and interact strongly, but then somehow disentangle themselves and go their separate ways. Some recent work [23,[30][31][32] has shown explicitly in certain examples how the gauge theory dynamics, at large N, leads to a local and causal description of semi-classical lowenergy supergravity. Building on this, we can argue that the information transfer to the outgoing Hawking radiation must take place near the black hole singularity from the point of view of infalling observers.…”

The Hadamard function and the Feynman propagator in the AdS/CFT correspondence

“…In order to extract the short-distance property we must expand G (1) around V = 1. For the spacelike separation σ > 0 with V = 1 + σ the last two terms in (16) …”

“…Thus we construct the Hadamard function in AdS d+1 expressed in terms of the invariant distance variable σ. The last two terms in (16) and (17) show contributions from the spacelike separation. The timelike region is composed of two parts which are characterized by θ(U − 1) and θ(1 − |V |).…”