Arithmetic Spacetime Geometry from String Theory

Details Arithmetic Spacetime Geometry from String Theory Arithmetic Spacetime Geometry from String Theory

2005-10-11

arxiv.org/abs/hep-th/0510091v1

Int.J.Mod.Phys. A21 (2006) 6323-6350

Physics

High Energy Physics

High Energy Physics - Theory

36 pages

Scientific paper

10.1142/S0217751X06034343

An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.

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