Gravitational backreaction of anti-D branes in the warped compactification

Abstract

We derive a low-energy effective theory for gravity with anti-D branes, which are essential to get de Sitter solutions in the type IIB string-warped compactification, by taking account of gravitational backreactions of anti-D branes. In order to see the effects of the self-gravity of anti-D branes, a simplified model is studied where a five-dimensional anti-de Sitter (AdS) spacetime is realized by the bulk cosmological constant and the 5-form flux, and anti-D branes are coupled to the 5-form field by Chern–Simon terms. The AdS spacetime is truncated by introducing UV and IR cut-off branes like the Randall–Sundrum model. We derive an effective theory for gravity on the UV brane and reproduce the familiar result that the tensions of the anti-D branes give potentials suppressed by the fourth power of the warp factor at the location of the anti-D branes. However, in this simplified model, the potential energy never inflates the UV brane, although the anti-D branes are inflating. The UV brane is dominated by dark radiation coming from the projection of the five-dimensional Weyl tensor, unless the moduli fields for the anti-D branes are stabilized. We comment on the possibility of avoiding this problem in a realistic string theory compactification.