Mirror manifolds in higher dimension


Journal Article

We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We isolate certain simplifying features present only in dimension three, and supply alternative methods that do not rely on these special characteristics and hence can be generalized to other dimensions. Although the moduli spaces for Calabi-Yau d-folds are not "special Kähler manifolds" when d>3, they still have a restricted geometry, and we indicate the new geometrical structures which arise. We formulate and apply procedures which allow for the construction of mirror maps and the calculation of order-by-order instanton corrections to Yukawa couplings. Mathematically, these corrections are expected to correspond to calculating Chern classes of various parameter spaces (Hilbert schemes) for rational curves on Calabi-Yau manifolds. Our mirror-aided calculations agree with those Chern class calculations in the limited number of cases for which the latter can be carried out with current mathematical tools. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra. © 1995 Springer-Verlag.

Full Text

Duke Authors

Cited Authors

  • Greene, BR; Morrison, DR; Plesser, MR

Published Date

  • November 1, 1995

Published In

Volume / Issue

  • 173 / 3

Start / End Page

  • 559 - 597

Electronic International Standard Serial Number (EISSN)

  • 1432-0916

International Standard Serial Number (ISSN)

  • 0010-3616

Digital Object Identifier (DOI)

  • 10.1007/BF02101657

Citation Source

  • Scopus