Investigating the Stability of a Nonsupersymmetric Landscape

Abstract

We investigate the classical stability of non-supersymmetric Freund-Rubin compactifications of Type IIB string theory on a product of three-dimensional Einstein spaces A_3 x B_3 with both NS-NS and R-R three-form fluxes turned on through A_3 and B_3, and a zero axion. This results in a three parameter family of AdS_4 vacua, with localized sources such as anti-three-branes or orientifold planes required to cancel the R-R four-form tadpole. We scan the entire space of such solutions for perturbative stability and find that anti-three-branes are unstable to a Jeans-like instability. For orientifold compactifications, we derive a precise criterion which the three dimensional Einstein spaces have to satisfy in order to be stable.