mirror symmetry
conjectured relation between pairs of Calabi–Yau manifolds; situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory
homological mirror symmetry
equivalence between the derived Fukaya category of a symplectic manifold and the derived category of coherent sheaves on a complex manifold
T-duality
duality in string theory in which compactifications on small spaces are equivalent to compactications on spaces of the inverse size; interchanges discrete KK momentum with winding number