Nonlinear waves in AdS/CFT correspondence

TL;DR

At strong coupling and large N, the paper analyzes radiation from an accelerated external charge in N=4 SYM using AdS/CFT. The radiation is encoded as a nonlinear wave on the string worldsheet in AdS5xS5, with an exact solution connecting boundary perturbations to bulk dynamics. The radiated energy is shown to be a local functional of the trajectory and follows the Liènard formula with coefficient A = sqrt(lambda)/(2 pi). This finding highlights an integrable-like structure of the worldsheet theory and motivates potential perturbative checks at finite coupling.

Abstract

We calculate in the strong coupling and large N limit the energy emitted by an accelerated external charge in ${\cal N}=4$ SU(N) Yang-Mills theory, using the AdS/CFT correspondence. We find that the energy is a local functional of the trajectory of the charge. It coincides up to an overall factor with the Lienard formula of the classical electrodynamics. In the AdS description the radiated energy is carried by a nonlinear wave on the string worldsheet for which we find an exact solution.

Figures (9)

• Figure 1: Timelike Wilson line.
• Figure 2: Moving one of the sources.
• Figure 3: $AdS_2\subset AdS_5$
• Figure 4: A right-moving wave.
• Figure 5: A linear wave.