Mirror symmetry is a duality among three-dimensional gauge theories with N=4 supersymmetry. It conjectures that pairs of theories with different gauge groups and matter contents flow to the same infrared conformal fixed points. This raises a puzzle as to how the duality acts on Wilson loop operators, which are labeled by gauge group representations.
The answer involves a second type of loop operators, called Vortex loops, which can be described by coupling certain supersymmetric quantum mechanics living on a line to the three-dimensional theories.
The map of loop operators relies on type IIB string theory brane constructions.

After an introduction on dualities and mirror symmetry, I will explain the main ideas of the mirror map for the loop operators.