Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-02-21
Commun.Math.Phys.173:559-598,1995
Physics
High Energy Physics
High Energy Physics - Theory
44 pages plus 3 tables using harvmac
Scientific paper
10.1007/BF02101657
We describe mirror manifolds in dimensions different from the familiar case of complex threefolds. We emphasize the simplifying features of dimension three and supply more robust methods that do not rely on such special characteristics and hence naturally generalize to other dimensions. The moduli spaces for Calabi--Yau $d$-folds are somewhat different from the ``special K\"ahler manifolds'' which had occurred for $d=3$, 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 results agree with those obtained by more traditional mathematical methods in the limited number of cases for which the latter analysis can be carried out. Finally, we make explicit some striking relations between instanton corrections for various Yukawa couplings, derived from the associativity of the operator product algebra.
Greene Brian R.
Morrison David R.
Plesser Ronen M.
No associations
LandOfFree
Mirror Manifolds in Higher Dimension does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Mirror Manifolds in Higher Dimension, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mirror Manifolds in Higher Dimension will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-124158