Semi-classical correlator for 1/4 BPS Wilson loop and chiral primary operator with large R-charge

TL;DR

This paper presents a holographic analysis of the correlation between a 1/4 BPS Wilson loop and a large R-charge local operator, constructing a rotating string solution that matches gauge theory predictions in the large R-charge limit.

Contribution

It introduces a new rotating string solution in AdS5×S5 that captures the correlation function of specific BPS operators with large R-charge, extending previous unstable configurations.

Findings

String solution reproduces correlation function at large R-charge.

A second, larger string solution is identified, reducing to an unstable configuration at J=0.

Gauge theory saddle point matches the string theory saddle point in the large R-charge limit.

Abstract

We study a holographic description for correlation function of 1/4 BPS Wilson loop operator and 1/2 BPS local operator carrying a large R-charge of order \sqrt \lambda. We construct a rotating string solution which is extended in S5 as well as in AdS5. The string solution preserves the 1/8 of the supersymmetry as expected from the gauge theory computation. By evaluating the string action including boundary terms we show that the string solution reproduces correlation function in large J \sim O(\sqrt \lambda) limit. In addition, we found the second solution for which the "size" of the string becomes larger than the radius of S5. In the case J=0, this solution reduces to the previously known unstable string configuration. The gauge theory side also contains a saddle point which is not on the steepest descent path. We show that the saddle point value matches for this case as well.