Supergravity Analysis of Hybrid Inflation Model from D3--D7 System

TL;DR

This paper investigates how hybrid inflation models derived from D3--D7 systems in string theory can achieve a sufficiently flat potential within supergravity, accounting for gravitational effects and stabilizing the geometry with fluxes.

Contribution

It demonstrates the viability of hybrid inflation in D3--D7 string models with supergravity, clarifying conditions for small slow-roll parameters and stabilization mechanisms.

Findings

Small slow-roll parameters achievable despite non-minimal Kahler potential

Stabilization of blown-up singularity geometry via 3-form fluxes

Conditions for positive vacuum energy in string vacua

Abstract

The slow-roll inflation is a beautiful paradigm, yet the inflaton potential can hardly be sufficiently flat when unknown gravitational effects are taken into account. However, the hybrid inflation models constructed in D = 4 N = 1 supergravity can be consistent with N = 2 supersymmetry, and can be naturally embedded into string theory. This article discusses the gravitational effects carefully in the string model, using D = 4 supergravity description. We adopt the D3--D7 system of Type IIB string theory compactified on K3 x T^2/Z_2 orientifold for definiteness. It turns out that the slow-roll parameter can be sufficiently small despite the non-minimal Kahler potential of the model. The conditions for this to happen are clarified in terms of string vacua. We also find that the geometry obtained by blowing up singularity, which is necessary for the positive vacuum energy, is stabilized by introducing certain 3-form fluxes.