The Langlands Program and String Modular K3 Surfaces

Details The Langlands Program and String Modular K3 Surfaces The Langlands Program and String Modular K3 Surfaces

2006-03-29

arxiv.org/abs/hep-th/0603234v1

Nucl.Phys.B771:143-166,2007

Physics

High Energy Physics

High Energy Physics - Theory

33 pages

Scientific paper

10.1016/j.nuclphysb.2007.01.027

A 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.

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