Classification of Modular Symmetries in Type IIB Flux Landscape

TL;DR

This paper investigates the modular symmetries of the type IIB flux landscape, focusing on symplectic basis transformations and their implications for flux vacua on toroidal orientifolds.

Contribution

It identifies specific modular symmetries, including a generalized S-transformation, and analyzes their effects on flux configurations and vacua in type IIB string theory.

Findings

Identified key modular symmetries affecting period vectors.

Analyzed flux transformations under these symmetries.

Explored implications for flux vacua stability and structure.

Abstract

In this work, we study modular symmetries in type IIB flux landscape by investigating symplectic basis transformations of period vectors on toroidal orbifolds. To fix explicit cycles of a third-cohomology basis regarding the untwisted complex structure modulus, which is necessary to construct the period vectors, we find that the following two symmetries are required for the period vectors: (i) ``Scaling duality '' which is a generalized $S$-transformation of $PSL(2, \mathbb{Z})$ and (ii) the modular symmetries to be consistent with symmetries derived from mass spectra of the closed string in type IIB string theory. Furthermore, by considering flux quanta on the cycles, we explore type IIB flux vacua on toroidal orientifolds and flux transformations under the modular symmetries of the period vectors.