Higher Derivative D-brane Couplings

This dissertation covers two different but related topics: the construction of consistent models in type IIB and heterotic string theories, and the higher derivative couplings for D-brane action, which will enable us to relate some models of type IIB to the heterotic side through duality chain. In the first part, we describe an alternative to the KKLT scenario, in which one can achieve de-Sitter space after fixing all moduli. We fix complex structure moduli and the axio-dilaton by deriving the stability conditions for the critical points of the no-scale scalar potential that governs the dynamics of the complex structure moduli and the axio-dilaton in compactifications of type IIB string theory on Calabi-Yau three-folds. In the second part, we show the existence of a class of flux backgrounds in heterotic string theory. The background metric we will consider is a T2 fibration over a K3 base times four-dimensional Minkowski space. Unbroken space-time supersymmetry determines all background fields except one scalar function which is related to the dilaton. The heterotic Bianchi identity gives the same differential equation for the dilaton, and we will discuss in detail the solvability of this equation for backgrounds preserving an N=2 supersymmetry. In the third part, we obtain the higher derivative D-brane action by using both linearized T-duality and string disc amplitude computation. We evaluate disc amplitude of one R-R field C^(p-3) and two NS-NS fields in the presence of a single Dp-brane in type II string theory. We obtain the action for the higher derivative brane interactions among one R-R field C^(p-3) and two NS-NS B-fields after carefully comparing the supergravity amplitudes with the corresponding string amplitude up to alpha^r2 order. We also show that these higher derivative brane couplings are invariant under both R-R and NS-NS B-field gauge transformations, and compatible with linear T-duality