Supergravity analysis of the hybrid inflation model from a D3-D7 system

The slow-roll inflation is a beautiful paradigm, yet the inflaton potentialcan hardly be sufficiently flat when unknown gravitational effects are takeninto account. However, the hybrid inflation models constructed in D = 4 N = 1supergravity can be consistent with N = 2 supersymmetry, and can be naturallyembedded into string theory. This article discusses the gravitational effectscarefully in the string model, using D = 4 supergravity description. We adoptthe D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2orientifold for definiteness. It turns out that the slow-roll parameter can besufficiently small despite the non-minimal Kahler potential of the model. Theconditions for this to happen are clarified in terms of string vacua. We alsofind that the geometry obtained by blowing up singularity, which is necessaryfor the positive vacuum energy, is stabilized by introducing certain 3-formfluxes.Comment: 21 pages; v3. a typo corrected, and some changes made in sections 4.1 and 4.2, accordingl