String Quantum Symmetries and the SL(2,Z) Group

TL;DR

This paper demonstrates that for Calabi-Yau three-folds with a single modulus, the quantum modular group of the string effective action cannot be SL(2,Z), based solely on the special Kähler structure of the moduli space.

Contribution

It provides a proof that the quantum modular group in this context is not SL(2,Z), using only geometric properties of the moduli space.

Findings

Quantum modular group is not SL(2,Z) for single modulus Calabi-Yau three-folds.

Proof relies solely on special Kähler structure, avoiding other assumptions.

Clarifies the symmetry structure of string effective actions in this setting.

Abstract

We prove, using arguments relying only on the "special K\"ahler" structure of the moduli space of the Calabi-Yau three-fold, that in the case of one single modulus the quantum modular group of the string effective action corresponding to Calabi-Yau vacua can not be SL(2,${Z\kern -4.6pt Z}$).