[Paper Review] On radiation by a heavy quark in N = 4 SYM

R. Baier|arXiv (Cornell University)|Jul 21, 2011

Black Holes and Theoretical Physics16 references4 citations

TL;DR

This paper re-examines radiation from a heavy quark in N = 4 supersymmetric Yang-Mills (SYM) theory at strong coupling using the AdS/CFT correspondence, proposing that only the irreversible, emission-dominant term of the radiation power—equivalent to the classical electromagnetic Schott term's counterpart—should be retained. The key contribution is showing that the strong-coupling radiation force in N = 4 SYM matches the structure of the Abraham-Lorentz force in classical electrodynamics, with orthogonality to velocity and vanishing for uniform acceleration, confirming consistency with known results in Mikhailov (2003er).

ABSTRACT

A short note on radiation by a moving classical particle in N = 4 supersymmetric Yang-Mills theory

Motivation & Objective

• To re-evaluate radiation patterns from a heavy quark in N = 4 SYM at strong coupling using the AdS/CFT correspondence.
• To resolve discrepancies in published radiation patterns by distinguishing irreversible emission from reversible Schott-type terms.
• To establish consistency between classical electrodynamics and N = 4 SYM radiation forces via the Abraham-Lorentz structure.
• To confirm that only the emission-dominant term (not total time derivative terms) contributes to irreversible energy loss in radiation.
• To verify agreement with Mikhailov (2003er) and prior results in synchrotron radiation and oscillating quark models.

Proposed method

• Applies the AdS/CFT correspondence in the supergravity limit to model radiation from a classical heavy quark in N = 4 SYM.
• Adopts the classical electrodynamics framework of Schwinger and Dirac to define radiation power via retarded and advanced fields.
• Decomposes radiation power into two components: $ P_{\text{emitt}} $, representing irreversible emission, and $ P_{\text{Schott}} $, a total time derivative term representing reversible energy exchange.
• Uses the condition $ v_\mu f^\mu = 0 $ (orthogonality of force to velocity) as a consistency check for the radiation force.
• Derives the strong-coupling radiation force $ f^\mu_{\text{SYM,strong}} = \frac{\sqrt{\lambda}}{2\pi} (a^\nu a_\nu v^\mu + \dot{a}^\mu) $, matching the Abraham-Lorentz form.
• Performs angular integration of the emission term $ P_{\text{emitt}} $ to compute time-averaged power and confirm agreement with known results.

Experimental results

Research questions

• RQ1 Why do published radiation patterns in N = 4 SYM at strong coupling differ from classical electrodynamics expectations?
• RQ2 Which component of the radiation power—emission or Schott-type term—represents irreversible energy loss?
• RQ3 Does the strong-coupling radiation force in N = 4 SYM retain the same structure as the Abraham-Lorentz force in classical electrodynamics?
• RQ4 How does the time-averaged radiation pattern for a quark in circular motion compare to known results in the literature?
• RQ5 Can the radiation force in N = 4 SYM be consistently derived from the emission term alone, enforcing orthogonality and vanishing for uniform acceleration?

Key findings

• The radiation force in N = 4 SYM at strong coupling is $ f^\mu_{\text{SYM,strong}} = \frac{\sqrt{\lambda}}{2\pi} (a^\nu a_\nu v^\mu + \dot{a}^\mu) $, matching the Abraham-Lorentz form.
• The force vanishes for uniformly accelerated motion, consistent with classical electrodynamics and the orthogonality condition $ v_\mu f^\mu = 0 $.
• Only the $ P_{\text{emitt}} $ term contributes to irreversible energy loss; the $ P_{\text{Schott}} $ term, being a total time derivative, does not.
• The time-averaged angular distribution of radiation power for synchrotron motion is $ \frac{dP_{\text{emitt}}(\bm{n})}{d\Omega} = \frac{\sqrt{\lambda}}{8\pi^{2}} \bm{a}^{2} \gamma^{5} \frac{1 + \frac{v^{2}}{2}\sin^{2}\Theta}{(\gamma^{2}\cos^{2}\Theta + \sin^{2}\Theta)^{5/2}} $, matching prior results.
• The total emitted power is $ P_{\text{emitt}} = \frac{\sqrt{\lambda}}{2\pi} [\gamma^{2} v \omega_{0}]^{2} $, consistent with Athanasiou et al. (2010pv), Hatta et al. (2011gh), and Mikhailov (2003er).