Three-Point Correlator of Heavy Vertex Operators for Circular Winding Strings in AdS5xS5

TL;DR

This paper computes a specific three-point correlator of heavy string states in AdS5xS5 using a Schwarz-Christoffel transformation, revealing conformal invariance and boundary behavior in a semiclassical framework.

Contribution

It introduces a novel semiclassical method employing Schwarz-Christoffel transformation to evaluate extremal three-point correlators for circular winding strings in AdS5xS5.

Findings

Derived a conformal invariant three-point correlator expression.

Mapped the string configuration to a complex plane with punctures.

Analyzed the marginality condition of the vertex operators.

Abstract

We consider an exremal three-point correlator of three heavy vertex operators for the circular winding string state with one large spin and one windining 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.