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

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 λ. 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 λ) 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.

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