|Topological Gauge Theory, S-duality and Mirror Symmetry|
d=4 supersymmetric gauge theories with Langlands-dual gauge groups are
conjectured to be equivalent on the nonperturbative level; this is
known as the S-duality conjecture. Performing a topological reduction
of these theories on a Riemann surface, one obtains a pair of
topological sigma-models whose target can be identified with the moduli
space of Hitchin equations.
S-duality implies that these sigma-models are related by mirror symmetry. This leads to a physical interpretation of the Geometric Langlands Program.