Two OneParameter Special Geometries
Abstract
The special geometries of two recently discovered CalabiYau threefolds with $h^{11}=1$ are analyzed in detail. These correspond to the 'minimal threegeneration' manifolds with $h^{21}=4$ and the `24cell' threefolds with $h^{21}=1$. It turns out that the onedimensional complex structure moduli spaces for these manifolds are both very similar and surprisingly complicated. Both have 6 hyperconifold points and, in addition, there are singularities of the PicardFuchs equation where the threefold is smooth but the Yukawa coupling vanishes. Their fundamental periods are the generating functions of lattice walks, and we use this fact to explain why the singularities are all at real values of the complex structure.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.08367
 Bibcode:
 2015arXiv151208367B
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 31 pages, 4 figures