  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.
