Anomalous dimension and local charges

TL;DR

This paper explores how deck transformations in AdS space relate to local conserved charges of classical strings and conjectures a similar connection for field theory operators, extending known relations involving anomalous dimensions and Yangian symmetry.

Contribution

It proposes that deck transformations are generated by an infinite sum of local charges and conjectures this relation extends to the dual field theory, generalizing previous results.

Findings

Deck transformations linked to local conserved charges in AdS

Conjecture of similar relations in dual field theory

Extension of anomalous dimension relations to Yangian algebra

Abstract

AdS space is the universal covering of a hyperboloid. We consider the action of the deck transformations on a classical string worldsheet in $AdS_5\times S^5$. We argue that these transformations are generated by an infinite linear combination of the local conserved charges. We conjecture that a similar relation holds for the corresponding operators on the field theory side. This would be a generalization of the recent field theory results showing that the one loop anomalous dimension is proportional to the Casimir operator in the representation of the Yangian algebra.