Integrability and higher loops in AdS/dCFT correspondence

We further study the correspondence between open semiclassical strings and long defect operators which is discussed in our previous work [Y. Susaki, Y. Takayama, K. Yoshida, hep-th/0410139]. We give an interpretation of the spontaneous symmetry breaking of SO(6)→SO(3)H×SO(3)V from the viewpoint of the Riemann surface by following the argument of Minahan. Then we use the concrete form of the resolvent for a single cut solution and compute the anomalous dimension of operators dual to an open pulsating string at three-loop level. In the string side we obtain the energy of the open pulsating string solution by semiclassical analysis. Both results agree at two-loop level but we find a three-loop discrepancy.