Abstract
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description. The Kähler function carries the complete geometric information on the theory. The non-vanishing bisectional curvature plays an important role in the construction. The new geometric formalism, with the nilpotent superfield representing the anti-D3 brane, allows a powerful generalization of the existing inflationary models based on supergravity. They can easily incorporate arbitrary values of the Hubble parameter, cosmological constant and gravitino mass. We illustrate it by providing generalized versions of polynomial chaotic inflation, T- and E-models of α-attractor type, disk merger. We also describe a multi-stage cosmological attractor regime, which we call cascade inflation.
Highlights
Effective supergravity inflationary models induced by anti-D3 brane interaction with the moduli fields in the bulk geometry have a geometric description
It has been realized during the last few years that both the construction of de Sitter vacua in string theory as well as building inflationary models is facilitated by the concept of an upliting D3 brane
The positive energy contribution sourced by a D3 brane in effective supergravity models is represented by a nilpotent multiplet S
Summary
We will explain here that the most general Kahler invariant Kahler function G depending on multiple Calabi-Yau moduli and on a nilpotent multiplet S can be reduced to the form we show in eq (1.2). Where KS, KS and GSS are non-holomorphic functions while f and g are holomorphic These are the most general Taylor expansions of the Kahler and superpotential due to the nilpotency condition S2 = 0. In terms of the redefined variables K0 = K0 + 2 log(|g|/|W0|), and KS = KS + f /g In this frame, the supersymmetry breaking is set by KS which we assume to be non-vanishing due to the nilpotency of S. The field redefinition dS = KSdS + ∂iKSSdT i + ∂jKSSdT j does not change the Kahler manifold of physical scalars It only affects the nilpotent part of the Kahler potential, which has a metric.
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