Integrability and Higher Loops in AdS/dCFT Correspondence

TL;DR

This paper investigates the integrability of open strings in AdS/dCFT, computes three-loop anomalous dimensions of defect operators, and identifies a discrepancy at three loops between string and gauge theory results.

Contribution

It provides a detailed three-loop calculation of anomalous dimensions for defect operators and explores the integrability structure in open string sectors.

Findings

Agreement at two-loop level between string and gauge theory

Discrepancy observed at three-loop level

Interpretation of symmetry breaking via Riemann surface

Abstract

We further study the correspondence between open semiclassical strings and long defect operators which is discussed in our previous work [hep-th/0410139]. We give an interpretation of the spontaneous symmetry breaking of SO(6)-> SO(3)_H x SO(3)_V from the viewpoint of the Riemann surface by following the argument of Minahan. Then we use the concrete form of the resolvent for a single cut solution and compute the anomalous dimension of operators dual to an open pulsating string at three-loop level. In the string side we obtain the energy of the open pulsating string solution by semiclassical analysis. Both results agree at two-loop level but we find a three-loop discrepancy.