Galois groups of uplifted de Sitter vacua

TL;DR

This paper investigates the Galois groups of polynomials related to critical points in type IIB string theory compactifications, revealing that de Sitter vacua correspond to unsolvable Galois groups, indicating a fundamental link between Galois theory and string vacua.

Contribution

It introduces a novel approach linking Galois groups to the stability of de Sitter vacua in string theory, providing new insights into their mathematical structure.

Findings

All de Sitter vacua from lifted AdS vacua have unsolvable Galois groups.

The study connects Galois theory with the construction of de Sitter solutions in string theory.

The results suggest a fundamental mathematical principle underlying the existence of certain string vacua.

Abstract

We compute the Galois group of a polynomial whose roots are determined by the critical points of a scalar potential in type IIB compactifications. We focus our study on certain perturbative models where it is feasible to construct a de Sitter vacuum within the effective theory by introducing non-geometric fluxes, D-branes, or non-BPS states. Our findings clearly show that all de Sitter vacua derived from lifting AdS stable vacua are associated with an unsolvable Galois group. This suggests a deeper connection between the fundamental principles of Galois theory and its applications in the construction of dS vacua.