Emergent spacetime from modular motives

TL;DR

This paper explores how spacetime geometry can be derived from string theory modular forms, linking Calabi-Yau motives and conformal field theories through L-functions and Galois representations.

Contribution

It extends the modular form construction of spacetime geometry to higher-dimensional Calabi-Yau varieties and motives, establishing a connection with conformal field theories.

Findings

Modular forms from omega motives relate to CFT characters.

L-functions serve as a bridge between motives and CFTs.

The approach applies to Calabi-Yau varieties of various dimensions.

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.