Three-point correlator of heavy vertex operators for circular winding strings in AdS5×S5

We consider an extremal three-point correlator of three heavy vertex operators for the circular winding string state with one large spin and one winding number in AdS5 and one large spin and one winding number in S5. We use a Schwarz-Christoffel transformation to compute semiclassically the extremal three-point correlator on a stationary string trajectory which is mapped to the complex plane with three punctures. It becomes a 4d conformal invariant three-point correlator on the boundary. We discuss the marginality condition of vertex operator.