Construction and couplings of mirror manifolds

We present an analysis of the conjectured existence of Calabi-Yau "mirror manifolds" for the case where the starting manifold is Y4,5. We construct mirror pairs with equal but opposite values for the Euler characteristic and the Hodge numbers h^2,1 and h^1,1 interchanged. In one particular example we show that the couplings of (1,1)-forms equal the couplings of (2,1)-forms in the mirror manifold, provided that a suitable limit is taken of the complex structure which corresponds to the large-radius limit appropriate for the mirror manifold. This leads to a determination, via deformation theory, of corrections to the topologically determined couplings of the (1,1)-forms. © 1990.

Duke Scholars

Author Paul Stephen Aspinwall Mathematics