On broken zero modes of a string world sheet, and a correlation function of a 1/4 BPS Wilson loop and a 1/2 BPS local operator

TL;DR

This paper analyzes the gravity dual of a correlation function between a 1/4 BPS Wilson loop and a 1/2 BPS local operator, emphasizing the role of broken zero modes in matching gauge theory results.

Contribution

It extends the understanding of broken zero modes' contributions to correlation functions in the gravity dual of BPS Wilson loops.

Findings

Agreement with gauge theory in the limit J << sqrt(lambda cos^2 theta_0)

Broken zero modes are crucial for correlation function calculations

Reconsideration of the gravity dual with zero mode contributions

Abstract

We reconsider a gravity dual of a 1/4 BPS Wilson loop. In the case of an expectation value of the Wilson loop, it is known that broken zero modes of a string world sheet in the gravity side play important roles in the limit $\lambda \to \infty$ with keeping the combination $\lambda \cos^2 \theta_0$ finite. Here, $\lambda$ is the 't Hooft coupling constant and $\theta_0$ is a parameter of the Wilson loop. In this paper, we reconsider a gravity dual of a correlation function between the Wilson loop and a 1/2 BPS local operator with R charge $J$. We take account of contributions coming from the same configurations of the above-mentioned broken zero modes. We find an agreement with the gauge theory side in the limit $J \ll \sqrt{\lambda \cos^2 \theta_0} $.