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.
Highlights
Within perturbative QCD, a similar behavior at large S holds for the twist-two operators built with quark fields in the fundamental representation of SU(N ), with the general structure
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
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
Summary
We consider a classical string embedded in the target space-time AdS5×S5 with metric gmn. It is well known that the AdS masses of local objects in AdS5, like supergravity fields or massive point-like particles, are proportional to the anomalous dimensions of the corresponding operators in the dual gauge theory [7, 8]. In the semiclassical limit where mR ≫ 1, the anomalous dimension of the CFT operator dual to this AdS particle is found as δ ≃ mR (see [19] for an explicit calculation) Note that this mass m is a property measured by a local observer in AdS5, in the same way as the infinitesimal string mass dmintroduced above. In view of the above, we conjecture that the string scale parameter γ should have a similar physical interpretation: for a semiclassical string with large spin, or R-charge, the quantity γ should be proportional to the anomalous dimension δ of the dual gauge theory operator.
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