Arithmetic Spacetime Geometry from String Theory

Abstract

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.

36 pages

References in corpus (7)

• Arithmetic Properties of Mirror Map and Quantum Coupling
• The Shimura-Taniyama Conjecture and Conformal Field Theory
• Mirror Maps, Modular Relations and Hypergeometric Series II
• Geometric Kac-Moody Modularity
• Arithmetic of Calabi-Yau Varieties and Rational Conformal Field Theory
• Complex Multiplication Symmetry of Black Hole Attractors
• Complex Multiplication of Exactly Solvable Calabi-Yau Varieties

Cited by in corpus (8)

• The Langlands Program and String Modular K3 Surfaces
• Emergent spacetime from modular motives
• Supergeometry and Arithmetic Geometry
• String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
• A modularity test for elliptic mirror symmetry
• String Automorphic Motives of nondiagonal Varieties
• K-Rational D-Brane Crystals
• Emergent spacetime and black hole probes from automorphic forms