# String theory and the Taniyama-Shimura conjecture

## TL;DR

This paper explores the connection between string theory, conformal field theory, and the Taniyama-Shimura conjecture, proposing a mathematical analogy that links physical models to elliptic curves and modular forms, with potential generalizations to F-theory.

## Contribution

It introduces a novel perspective linking string theory and conformal field theory to the Taniyama-Shimura conjecture, suggesting a deep mathematical structure underlying physical theories.

## Key findings

- String worldsheet corresponds to elliptic curves.
- Partition functions in string theory relate to modular forms.
- Potential extension to F-theory generalizes the framework.

## Abstract

The worldsheet of the string theory, which consisting of 26 free scalar fields in Minkowski space, is two dimensional conformal field theory. If we denote the two dimension conformal field theory by elliptic curve and denote the partition function of string theory by modular form, then the relation between conformal field theory and the string theory can be represented as the Taniyama-Shimura conjecture. Moreover, it also can be generalized to the $F$-theory.