Stability of $Ad{S}_{p}x{S}^{n}x{S}^{q-n}$ Compactifications

Abstract

We examine the stability of ${\mathrm{AdS}}_p\times {\mathrm{S}}^n\times {\mathrm{S}}^{q-n}$. 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 ${\mathrm{AdS}}_p$ 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 $q\ge 9$.

Comments: 6 pages, 3 figures