Instabilities in scale-separated Casimir vacua

TL;DR

This paper explores the stability of scale-separated Casimir vacua in flux compactifications, highlighting both perturbative and non-perturbative instabilities in these geometries.

Contribution

It provides an explicit example in eleven-dimensional supergravity and analyzes the stability of these vacua under various deformations.

Findings

Identifies perturbative instabilities in Casimir vacua.

Discovers non-perturbative instabilities affecting these geometries.

Demonstrates the challenges in achieving stable scale separation in flux compactifications.

Abstract

Parametric scale separation is notoriously difficult to achieve in flux compactifications of gravitational effective theories. An appealing alternative to conventional Freund-Rubin vacua involves Ricci-flat internal manifolds, where the energy supplied by fluxes is balanced not by curvature but by the Casimir energy. The internal volume can be stabilized by this mechanism producing anti-de Sitter geometries with parametric scale separation, including an explicit example in eleven-dimensional supergravity. We study deformations of these geometries, showing the presence of perturbative and non-perturbative instabilities.