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Journal Articles Journal of High Energy Physics Year : 2014

## Anomalous dimensions from rotating open strings in AdS/CFT

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Nelson R. F. Braga
• Function : Author
Edmond Iancu
• Function : Author

#### 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.

### Dates and versions

cea-01011623 , version 1 (18-10-2022)

### Licence

Attribution - CC BY 4.0

### Identifiers

• HAL Id : cea-01011623 , version 1
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• DOI :

### Cite

Nelson R. F. Braga, Edmond Iancu. Anomalous dimensions from rotating open strings in AdS/CFT. Journal of High Energy Physics, 2014, 2014, pp.104. ⟨10.1007/JHEP08(2014)104⟩. ⟨cea-01011623⟩

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