One-loop correction to the energy of a wavy line string in AdS_5

We consider a computation of one-loop AdS_5 x S^5 superstring correction to the energy radiated by the end-point of a string which moves along a wavy line at the boundary of AdS_5 with a small transverse acceleration (the corresponding classical solution was described by Mikhailov in hep-th/0305196). We also compute the one-loop effective action for an arbitrary small transverse string fluctuation background. It is related by an analytic continuation to the Euclidean effective action describing one-loop correction to the expectation value of a wavy Wilson line. We show that both the one-loop contribution to the energy and to the Wilson line are controlled by the subleading term in the strong-coupling expansion of the function B(\lambda) as suggested by Correa, Henn, Maldacena and Sever in arXiv:1202.4455.