A tunneling picture of dual giant Wilson loop

TL;DR

This paper explores a rotating dual giant Wilson loop in AdS space, showing it comprises a Wilson loop and a graviton, and computes its classical action to match gauge theory predictions.

Contribution

It provides a tunneling framework to analyze dual giant Wilson loops, connecting their gravity solutions with gauge theory operators and calculating their expectation values.

Findings

The Euclidean action reproduces the Wilson loop expectation value.

The solution combines a Wilson loop with a dual giant graviton.

The tunneling approach links gravity solutions to gauge theory results.

Abstract

We further discuss a rotating dual giant Wilson loop (D3-brane) solution constructed in Lorentzian AdS by Drukker et al. The solution is shown to be composed of a dual giant Wilson loop and a dual giant graviton by minutely examining its shape. This observation suggests that the corresponding gauge-theory operator should be a k-th symmetric Wilson loop with the insertions of dual giant graviton operators. To support the correspondence, the classical action of the solution should be computed and compared with the gauge-theory result. For this purpose we first perform a Wick rotation to the Lorentzian solution by following the tunneling prescription and obtain Euclidean solutions corresponding to a circular or a straight-line Wilson loop. In Euclidean signature boundary terms can be properly considered in the standard manner and the classical action for the Euclidean solutions can be evaluated. The result indeed reproduces the expectation value of the k-th symmetric Wilson loop as well as the power-law behavior of the correlation function of dual giant graviton operators.