# Type IIB flux vacua and tadpole cancellation

## TL;DR

This paper investigates flux vacua in type IIB orientifold compactifications, revealing that consistent solutions with stabilized moduli are rare and exhibit complex structures constrained by tadpole cancellation.

## Contribution

It provides a detailed analysis of flux vacua in a specific orientifold model, highlighting the scarcity of solutions satisfying all physical and consistency conditions.

## Key findings

- Large flux contributions are required for solutions but are disfavored by tadpole constraints.
- Solutions with stabilized moduli are very rare among all possible vacua.
- The solution space exhibits voids and is concentrated on submanifolds.

## Abstract

We consider flux vacua for type IIB orientifold compactifications and study their interplay with the tadpole-cancellation condition. As a concrete example we focus on $\mathbb T^6/\mathbb Z_2\times \mathbb Z_2$, for which we find that solutions to the F-term equations at weak coupling, large complex structure and large volume require large flux contributions. Such contributions are however strongly disfavored by the tadpole-cancellation condition. We furthermore find that solutions which stabilize moduli in this perturbatively-controlled regime are only a very small fraction of all solutions, and that the space of solutions is not homogenous but shows characteristic void structures and vacua concentrated on submanifolds.