Wilson loops in 3-dimensional N=6 supersymmetric Chern-Simons Theory and their string theory duals

TL;DR

This paper investigates Wilson loops in 3D N=6 supersymmetric Chern-Simons theory, calculating their expectation values at weak and strong coupling, and identifies their string theory duals as fundamental strings, D2-branes, and D6-branes.

Contribution

It constructs supersymmetric Wilson loop operators in the theory, computes their expectation values at two-loop order, and matches these with string theory dual solutions.

Findings

Weak coupling expectation values computed up to 2-loop order.

Strong coupling duals identified as fundamental strings, D2-branes, and D6-branes.

Dual solutions match symmetries, charges, and supersymmetries of the field theory operators.

Abstract

We study Wilson loops in the three-dimensional N=6 supersymmetric Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena, that is conjectured to be dual to type IIA string theory on AdS_4 x CP^3. We construct loop operators in the Chern-Simons theory which preserve 1/6 of the supercharges and calculate their expectation value up to 2-loop order at weak coupling. The expectation value at strong coupling is found by constructing the string theory duals of these operators. For low dimensional representations these are fundamental strings, for high dimensional representations these are D2-branes and D6-branes. In support of this identification we demonstrate that these string theory solutions match the symmetries, charges and the preserved supersymmetries of their Chern-Simons theory counterparts.