We present the main results of hep-th/1106.5412 and hep-th/1202.5292. This includes both the computation of the expectation value of the N=4 SU(N) SYM Lagrangian density operator in the presence of an infinitely heavy static particle in the symmetric representation and that of the energy radiated by an inﬁnitely massive particle transforming in the symmetric or antisymmetric representation of the gauge group, and moving in the vacuum, to all orders in 1/N and for large ’t Hooft coupling. Next, we argue that the agreement between these two results go beyond the probe approximation, which leads us to propose an exact formula for the total energy loss by radiation of a heavy particle in the fundamental representation.