2005/10/11 by Rolf Schimmrigk
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #Homotopy and Cohomology in Algebraic Topology #hep-th
paper · pdf · doi:10.1142/s0217751x06034343
published as Int.J.Mod.Phys. A21 (2006) 6323-6350 · 36 pages
arxiv created 2005/10/11 · openalex publication_date 2006/12/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
An arithmetic framework for 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 space–time, and that the geometry is uniquely determined by the two-dimensional field theory on the worldsheet. 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.