String Theory Group

Calabi-Yau geometry

Calabi-Yau (CY) 3-folds are complex spaces (with 3 complex or equivalently 6 real dimensions) that are vacuum solutions of the spatial Einstein equations. CY manifolds come in families smoothly related to each other by deformation parameters controlling their shape and size. Using toric geometry one can construct a large number of CY three-folds. The power of the toric description consists in the fact that geometry can be encoded in terms of combinatoric data. For the construction of explicit string theory models a systematic investigation of the topological properties of toric CY manifolds is of main relevance. Members of our group (Maximilian Kreuzer and Harald Skarke) produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions. For the science community we provide access to this database in form of our Calabi-Yau data website.

Left: The torus, the only compact CY in 1 complex dimension.	Right:A 2-dimensional visualisation of the quintic CY 3-fold.

Another issue involving Calabi-Yau manifolds is the study of mirror symmetry. This is a string duality that arises from the compactification of string theory on two different CY manifolds (forming a mirror pair) which leads to the same 4-dimensional physics.