Undulating Strings and Gauge Theory Waves

TL;DR

The paper investigates how oscillations of strings in AdS, dual to external heavy quarks in N=4 SYM, manifest as time-dependent gauge fields on the boundary. Using the GKPW prescription, Callan and Guijosa compute bulk dilaton fields sourced by oscillating strings and D5-brane baryons, translating them into boundary expectations for the operator O_F^2. They show that static fields for isolated quarks reproduce known near-field behavior while dynamical string fluctuations generate boundary waves that are superpositions of delayed signals, with caustics and phase delays reflecting the bulk propagation along the string; for color-neutral configurations, static fields decay as faster powers of distance, and baryons carry an extra N factor. A central open issue is energy conservation: whether these bulk-induced boundary waves correspond to true radiation requires including backreaction and evaluating the boundary energy-momentum tensor, highlighting a subtle aspect of energy flow in holography and outlining directions for future work.

Abstract

We study some dynamical aspects of the correspondence between strings in AdS space and external heavy quarks in N=4 SYM. Specifically, by examining waves propagating on such strings, we make some plausible (and some surprising) inferences about the time-dependent fields produced by oscillating quarks in the strongly-coupled gauge theory. We point out a puzzle regarding energy conservation in the SYM theory. In addition, we perform a similar analysis of the gauge fields produced by a baryon (represented as a D5-brane with string-like extension in AdS space) and compare and contrast with the gauge fields produced by a quark-antiquark pair (represented as a string looping through AdS space).

Figures (4)

• Figure 1: A Nambu-Goto string lying along a geodesic, with its two endpoints on the boundary.
• Figure 2: Any given point on the boundary receives radiation from each point along the string. As a result, the gauge theory wave is a superposition of components with all possible time delays. See text for discussion.
• Figure 3: Any given point on the boundary receives radiation from each point along the 'bent' string, with a corresponding time delay. Notice that the boundary projection of wavefronts given off at a point $z'$ on the string yields a spherical wave which appears to originate from $\hbox{$\vec{X}$}_{s}(z')$. See text for discussion.
• Figure 4: From the $AdS_{5}$ perspective, the baryon is a 'fat string' extending from the boundary up to $z=z_{m}$. At each value of $z$, the fivebrane lies at a different polar angle on the five-sphere.