# Department of Physics and Astronomy

Permanent link for this collectionhttps://hdl.handle.net/2022/22354

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# Browsing Department of Physics and Astronomy by Subject "Calabi-Yau manifolds"

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Item Complex Multiplication Symmetry of Black Hole Attractors(Elsevier, 2003) Lynker, Monika; Periwal, Vipul; Schimmrigk, RolfWe show how Moore’s observation, in the context of toroidal compactifications in type IIB string theory, concerning the complex multiplication structure of black hole attractor varieties, can be generalized to Calabi-Yau compactifications with finite fundamental groups. This generalization leads to an alternative general framework in terms of motives associated to a Calabi-Yau variety in which it is possible to address the arithmetic nature of the attractor varieties in a universal way via Deligne’s period conjecture.Item The Langlands Program and String Modular K3 Surfaces(Nuclear Physics B, 2006-03) Schimmrigk, RolfA number theoretic approach to string compactification is developed for Calabi-Yau hypersurfaces in arbitrary dimensions. The motivic strategy involved is illustrated by showing that the Hecke eigenforms derived from Galois group orbits of the holomorphic two-form of a particular type of K3 surfaces can be expressed in terms of modular forms constructed from the worldsheet theory. The process of deriving string physics from spacetime geometry can be reversed, allowing the construction of K3 surface geometry from the string characters of the partition function. A general argument for K3 modularity follows from mirror symmetry, in combination with the proof of the Shimura-Taniyama conjecture.