Duality in Calabi-Yau moduli space

Abstract

We describe a duality in the moduli space of string vacua which pairs topologically distinct Calabi-Yau manifolds and shows that the yield isomorphic conformal theories. At the level of the geometrical description, this duality interchanges the roles of Kähler and complex structure moduli and thus pairs manifolds whose Euler numbers differ by χ → − χ. Amongst the interesting implications of this duality is the conclusion that by using both manifolds of a “mirror pair” the 27³ and $\text{27}{}^3$ couplings can be computed exactly by lowest-order geometrical calculations.