We consider a heavy probe coupled to a general four-dimensional conformal field theory, and argue that a variety of interesting quantities are determined in terms of a single function, the Bremsstrahlung function, that depends on the probe and on the theory. For the particular case of a heavy quark coupled to N=4 super Yang Mills, we use localization techniques to determine the corresponding Bremsstrahlung function exactly. As an application, we use this exact result to test how well does SUGRA compute transport coefficients.