Correlators of Vertex Operators for Circular Strings with Winding Numbers in AdS5xS5

TL;DR

This paper calculates semiclassical two- and three-point correlators of vertex operators for circular string states with winding in AdS5xS5, linking conformal invariance with Virasoro constraints and exploring relations to string state dimensions.

Contribution

It provides a semiclassical computation of correlators for circular strings with winding, connecting marginality conditions to Virasoro constraints and analyzing three-point functions involving dilaton operators.

Findings

Correlators satisfy Virasoro constraints.

Two-point correlator matches conformal invariance expectations.

Three-point correlator relates to string state dimension derivatives.

Abstract

We compute semiclassically the two-point correlator of the marginal vertex operators describing the rigid circular spinning string state with one large spin and one windining number in AdS_5 and three large spins and three winding numbers in S^5. The marginality condition and the conformal invariant expression for the two-point correlator obtained by using an appropriate vertex operator are shown to be associated with the diagonal and off-diagonal Virasoro constraints respectively. We evaluate semiclassically the three-point correlator of two heavy circular string vertex operators and one zero-momentum dilaton vertex operator and discuss its relation with the derivative of the dimension of the heavy circular string state with respect to the string tension.