Supersymmetric Wilson Loops in Diverse Dimensions

TL;DR

This paper investigates supersymmetric Wilson loops across various dimensions, demonstrating their trivial vacuum expectation values at weak coupling and constructing their dual string solutions, revealing insights into gauge/gravity duality and anomalies.

Contribution

It extends the understanding of supersymmetric Wilson loops in diverse dimensions, providing explicit dual string solutions and analyzing their properties, including the vanishing of their regularized actions.

Findings

Wilson loops have trivial vacuum expectation values to second order in coupling.

Explicit dual string solutions with vanishing regularized action are constructed.

Generalized framework of calibrated surfaces proves vanishing of string action for arbitrary loops.

Abstract

We consider supersymmetric Wilson loops a la Zarembo in planar supersymmetric Yang-Mills theories in diverse dimensions. Using perturbation theory we show that these loops have trivial vacuum expectation values to second order in the 't Hooft coupling. We review the known superspace results which, for specific dimensions, extend this triviality to all orders in the 't Hooft coupling. Using the gauge/gravity correspondence, we construct the explicit dual fundamental string solutions corresponding to these Wilson loops for the case of circular geometry. We find that the regularized action of these string solutions vanishes. We also generalize the framework of calibrated surfaces to prove the vanishing of the regularized action for loops of general geometry. We propose a possible string-side manifestation of the gauge theory generalized Konishi anomaly in seven dimensions.