Streamlined Supergravity

TL;DR

The paper develops a streamlined N=1 supergravity framework that uses a nilpotent chiral multiplet to realize any desired bosonic scalar potential by tuning the nilpotent sector’s Kähler metric, for arbitrary Kähler potentials of the physical scalars. It derives explicit formulas for the nilpotent-sector metric and demonstrates how to realize $V(z^i, \bar z^{\bar i})$ with $W = W_0 + sF_s$, independent of the physical superpotential, enabling flexible inflationary model-building. The authors provide concrete inflationary realizations in hyperbolic geometry (E-models and T-models) as well as polynomial/pole inflation in both half-plane and disk variables, including axion stabilization, and discuss consistency and gauge-fixing to ensure a well-defined theory. This approach broadens the toolkit for embedding phenomenological bosonic models, including de Sitter solutions and moduli stabilization, directly into supergravity with maximal freedom in kinetic terms and scalar potentials.

Abstract

The textbook N=1 supergravity has an F-term potential depending on a superpotential $W(z_i)$ and a Kahler potential $K(z^i, \bar z^{\bar i})$, with the scalar potential $V(z^i, \bar z^{\bar i})=e^K (|DW|^2 - 3 |W|^2)$. In this approach, it is not always easy to find the potential $V(z^i, \bar z^{\bar i})$ with the required properties. We show that in supergravity with a nilpotent superfield and with any Kahler potential $K(z^i, \bar z^{\bar i} )$ one can obtain any desired potential $V(z^i, \bar z^{\bar i})$ by a proper choice of the Kahler metric of the nilpotent superfield. This construction is particularly suitable for cosmological and particle physics applications, which may require maximal freedom in the choice of kinetic terms and scalar potentials.