Anomalous dimensions from rotating open strings in AdS/CFT

TL;DR

This paper proposes a new way to relate the anomalous dimensions of certain gauge theory operators to the length of semiclassical rotating strings in AdS space, extending the AdS/CFT dictionary at strong coupling.

Contribution

It introduces a conjecture linking anomalous dimensions to string proper length, validated for various string configurations, and applies it to compute dimensions of operators with fundamental matter.

Findings

Anomalous dimension proportional to string proper length for rotating strings.

Logarithmic spin dependence of anomalous dimensions for open strings with fundamental matter.

Operator properties are independent of the quark mass scale, consistent with physical expectations.

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.