# Anomalous dimensions from rotating open strings in AdS/CFT

Abstract : We propose a new entry within the dictionary of the AdS/CFT duality at strong coupling: in the limit of a large spin or a large R-charge, the anomalous dimension of the gauge theory operator dual to a semiclassical rotating string is proportional to the string proper length. This conjecture is motivated by a generalization to strings of the rule for computing anomalous dimensions of massive particles and supergravity fields in the anti-de Sitter space. We show that this proportionality holds for a rotating closed string in global AdS space, representing a high spin operator made of fields in the adjoint representation. It is also valid for closed strings rotating in $S^5$ (representing operators with large R-charge), for closed strings with multiple AdS spin, and for giant magnons. Based on this conjecture, we calculate the anomalous dimension $\delta$ of operators made of fields in the fundamental representation, associated with high spin mesons, and which are represented by rotating open strings attached to probe D7-branes. The result is a logarithmic dependence upon the spin, $\delta\sim \sqrt{\lambda}\ln S$, similar to the closed string case. We show that the operator properties --- anomalous dimension and spin --- are obtained from measurements made by a local observer in the anti-de Sitter space. For the open string case, this ensures that these quantities are independent of the mass scale introduced by the D7-branes (the quark mass), as expected on physical grounds. In contrast, properties of the gauge theory states, like the energy, correspond to measurements by a gauge theory observer and depend upon the mass scale --- once again, as expected.
Document type :
Preprints, Working Papers, ...

https://hal-cea.archives-ouvertes.fr/cea-01011623
Contributor : Emmanuelle de Laborderie <>
Submitted on : Tuesday, June 24, 2014 - 11:13:20 AM
Last modification on : Wednesday, September 12, 2018 - 2:14:07 PM

### Identifiers

• HAL Id : cea-01011623, version 1
• ARXIV : 1405.7388

### Citation

Nelson R. F. Braga, Edmond Iancu. Anomalous dimensions from rotating open strings in AdS/CFT. 2014. ⟨cea-01011623⟩

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