Emergent spacetime from modular motives

Abstract

The program of constructing spacetime geometry from string theoretic modular forms is extended to Calabi-Yau varieties of dimensions two, three, and four, as well as higher rank motives. Modular forms on the worldsheet can be constructed from the geometry of spacetime by computing the L-functions associated to omega motives of Calabi-Yau varieties, generated by their holomorphic $n-$forms via Galois representations. The modular forms that emerge from the omega motive and other motives of the intermediate cohomology are related to characters of the underlying rational conformal field theory. The converse problem of constructing space from string theory proceeds in the class of diagonal theories by determining the motives associated to modular forms in the category of motives with complex multiplication. The emerging picture indicates that the L-function can be interpreted as a map from the geometric category of motives to the category of conformal field theories on the worldsheet.

40 pages

References in corpus (6)

• The Arithmetic of Calabi--Yau Manifolds and Mirror Symmetry
• The Langlands Program and String Modular K3 Surfaces
• Construction and examples of higher-dimensional modular Calabi-Yau manifolds
• Arithmetic Spacetime Geometry from String Theory
• Geometric Kac-Moody Modularity
• A modularity test for elliptic mirror symmetry

Cited by in corpus (12)

• Eisenstein series and automorphic representations
• $G_4$ Flux, Algebraic Cycles and Complex Structure Moduli Stabilization
• String Modular Phases in Calabi-Yau Families
• A General Framework of Automorphic Inflation
• String-theory Realization of Modular Forms for Elliptic Curves with Complex Multiplication
• Automorphic Black Holes as Probes of Extra Dimensions
• String Automorphic Motives of nondiagonal Varieties
• Automorphic Black Hole Entropy
• Black Hole Probes of Automorphic Space
• Motivic L-Function Identities from CFT and Arithmetic Mirror Symmetry
• K-Rational D-Brane Crystals
• Rank-2 attractors and Fermat type CY $n$-folds