Stability of $AdS_p x S^n x S^{q-n}$ Compactifications

TL;DR

This paper analyzes the stability of certain anti-de Sitter space compactifications involving spheres, confirming stability for specific dimensions using effective theories and energy theorems.

Contribution

It derives the effective action for dilatonic compactifications and applies the positive energy theorem to establish stability criteria.

Findings

No lower mass bound for q<9

Stability confirmed for q≥9

Effective action derived for non-linear fluctuations

Abstract

We examine the stability of ${\rm AdS}_p \times {\rm S}^n \times {\rm S}^{q-n}$. The initial data constructed by De Wolfe et al \cite{Gary} has been carefully analyised and we have confirmed that there is no lower bound for the total mass for $q< 9$. The effective action on ${\rm AdS}_p$ has been derived for dilatonic compactification of the system to describe the non-linear fluctuation of the background space-time. The stability is discussed applying the positive energy theorem to the effective theory on AdS, which again shows the stability for $q \geq 9$.