Energy-Spin Trajectories in AdS_5 x S^5 from Semiclassical Vertex Operators

TL;DR

This paper explores the connection between vertex operators and classical spinning string solutions in AdS_5 x S^5, demonstrating their equivalence in the semiclassical limit and deriving energy-quantum number relations.

Contribution

It establishes a correspondence between vertex operators and classical string solutions in AdS_5 x S^5, revealing their equivalence in the semiclassical regime and analyzing the marginality conditions.

Findings

Vertex operators define singular solutions matching classical strings.

Marginality conditions relate energy and quantum numbers.

Vertex operators in AdS_5 x S^5 may require complex expressions.

Abstract

We study the relation between vertex operators in AdS_5 x S^5 and classical spinning string solutions. In the limit of large quantum numbers the treatment of vertex operators becomes semiclassical. In this regime, a given vertex operator carrying a certain set of quantum numbers defines a singular solution. We show in a number of examples that this solution coincides with the classical string solution with the same quantum numbers but written in a different two-dimensional coordinate system. The marginality condition imposed on an operator yields a relation between the energy and the other quantum numbers which is shown to coincide with that of the corresponding classical string solution. We also argue that in some cases vertex operators in AdS_5 x S^5 cannot be given by expressions similar to the ones in flat space and a more involved consideration is required.