I will present a rigorous formulation and proof of the 1/N
expansion for SO(N) lattice gauge theory in any dimension. The 1/N
expansion for lattice gauge theories was invented by Gerardus 't Hooft
more than forty years ago in the physics literature. Rigorous proofs
were established in various contexts, but not for the original setting
of lattice gauge theories. It turns out that the terms in the
expansion are expressible as sums over trajectories of strings in a
lattice string theory, establishing an explicit gauge-string duality.
The trajectories trace out surfaces of genus zero for the first term
in the expansion, and surfaces of higher genus for the higher terms.
This is joint work with Jafar Jafarov.