1/4 BPS circular loops, unstable world-sheet instantons and the matrix model

TL;DR

This paper studies multiple saddle points in Wilson loop calculations within AdS/CFT, revealing a connection to matrix models and proposing a new BMN-like limit for nearly BPS operators.

Contribution

It identifies multiple saddle points for 1/4 BPS Wilson loops and links their contributions to a free matrix model, extending understanding of strong coupling behavior.

Findings

Existence of two 1/4 BPS string solutions, one stable and one unstable.

Perturbative expansion is captured by a free matrix model.

Proposal of a new BMN-like limit for nearly BPS Wilson loops.

Abstract

The standard prescription for computing Wilson loops in the AdS/CFT correspondence in the large coupling regime and tree-level involves minimizing the string action. In many cases the action has more than one saddle point as in the simple example studied in this paper, where there are two 1/4 BPS string solutions, one a minimum and the other not. Like in the case of the regular circular loop the perturbative expansion seems to be captured by a free matrix model. This gives enough analytic control to extrapolate from weak to strong coupling and find both saddle points in the asymptotic expansion of the matrix model. The calculation also suggests a new BMN-like limit for nearly BPS Wilson loop operators.