UV/IR Relations in AdS Dynamics

TL;DR

The paper analyzes how long-distance AdS dynamics map to high-energy boundary behavior by identifying two distinct distance–energy relations, with conformal cases yielding linear mappings and nonconformal cases altering the functional form. Through careful examination of D3-, M2-, M5-brane geometries and nonconformal D$p$-branes, it shows that holographic energy scales, probe energies, and effective couplings must be distinguished when interpreting UV/IR relations and state counting. The results connect holographic prescriptions to black hole entropy counts and highlight the limits of simple renormalization-group intuition in AdS/CFT, especially for $p \ge 5$ and $p = 6$, where dual descriptions can decouple into separate sectors. Overall, the work clarifies how bulk gravity, probe dynamics, and gauge theory degrees of freedom interrelate across conformal and nonconformal backgrounds, sharpening the conceptual foundations of holography.

Abstract

We point out that two distinct distance--energy relations have been discussed in the AdS/CFT correspondence. In conformal backgrounds they differ only in normalization, but in nonconformal backgrounds they differ in functional form. We discuss the relation to probe processes, the holographic principle, and black hole entropies.