Conformal SO(2, 4) transformations of the one-cusp Wilson loop surface

By applying the conformal SO(2, 4) transformations to the elementary one-cusp Wilson loop surface we construct various two-cusp and four-cusp Wilson loop surface configurations in AdS5 and demonstrate that they solve the string equations of the Nambu-Goto string action. The conformal boosts of the basic four-cusp Wilson loop surface with a square-form projection generate various four-cusp Wilson loop surfaces with projections of the rescaled square, the rhombus and the trapezium, on which surfaces the classical Euclidean Nambu-Goto string actions in the IR dimensional regularization are evaluated.