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 δ 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, , 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.
- Publication:
-
Journal of High Energy Physics
- Pub Date:
- August 2014
- DOI:
- 10.1007/JHEP08(2014)104
- arXiv:
- arXiv:1405.7388
- Bibcode:
- 2014JHEP...08..104B
- Keywords:
-
- AdS-CFT Correspondence;
- Gauge-gravity correspondence;
- High Energy Physics - Theory
- E-Print:
- V2: two related references included