Wilson loops T-dual to Short Strings

TL;DR

This paper demonstrates a T-duality relation between closed string solutions in AdS space and open string solutions ending on Wilson loops, linking string dynamics to gauge theory observables.

Contribution

It establishes a novel connection between small, short closed strings and open strings ending on Wilson loops via T-duality, revealing how string properties encode gauge theory data.

Findings

Short strings map to open strings ending on wavy Wilson lines.

Wilson loop shape relates to the closed string crossing the horizon.

Energy and spin of strings are encoded in Wilson loop properties.

Abstract

We show that closed string solutions in the bulk of AdS space are related by T-duality to solutions representing an open string ending at the boundary of AdS. By combining the limit in which a closed string becomes small with a large boost, we find that the near-flat space short string in the bulk maps to a periodic open string world surface ending on a wavy line at the boundary. This open string solution was previously found by Mikhailov and corresponds to a time-like near BPS Wilson loop differing by small fluctuations from a straight line. A simple relation is found between the shape of the Wilson loop and the shape of the closed string at the moment when it crosses the horizon of the Poincare patch. As a result, the energy and spin of the closed string are encoded in properties of the Wilson loop. This suggests that closed string amplitudes with one of the closed strings falling into the Poincare horizon should be dual to gauge theory correlators involving local operators and a Wilson loop of the T-dual ("momentum") theory.