S-duality of boundary conditions and the Geometric Langlands program

Understand

Maximally supersymmetric gauge theory in four dimensions admits local boundary conditions which preserve half of the bulk supersymmetries.

• The S-duality of the bulk gauge theory can be extended in a natural fashion to act on such half-BPS boundary conditions.
• The purpose of this note is to explain the role these boundary conditions can play in the Geometric Langlands program.
• In particular, we describe how to obtain pairs of Geometric Langland dual objects from S-dual pairs of half-BPS boundary conditions.