Exact momentum fluctuations of an accelerated quark in N=4 super Yang-Mills

TL;DR

This paper derives an exact expression for the momentum fluctuations of an accelerated quark in conformal field theories, using the Bremsstrahlung function, and applies it specifically to N=4 SYM to explore its implications.

Contribution

It provides an exact relation between momentum fluctuations and the Bremsstrahlung function for accelerated quarks in conformal theories, with explicit results for N=4 SYM.

Findings

Exact momentum fluctuation expression linked to Bremsstrahlung function.

Explicit momentum diffusion coefficient for N=4 SU(N) SYM.

Insights into heavy quark behavior in super Yang-Mills plasma.

Abstract

In this work we consider a heavy quark moving with constant proper acceleration in the vacuum of any four dimensional conformal field theory. We argue that the two-point function of its momentum fluctuations is exactly captured by the Bremsstrahlung function that gives the total radiated power. For the particular case of N=4 SU(N) SYM this function is exactly known, so in this case we obtain an explicit expression for the momentum diffusion coefficient, and check that various limits of this result are reproduced by probe computations in AdS_5. Finally, we evaluate this transport coefficient for a heavy quark accelerated in the vacuum of N=4 SU(3) SYM, and comment on possible lessons of our results for the study of heavy quarks traversing the super Yang-Mills plasma.