Unitarity constraint on the K\"ahler curvature

TL;DR

This paper investigates how unitarity constraints in supersymmetric theories determine the sign of quartic terms in the K"ahler potential, impacting the stability of inflationary and supersymmetry-breaking models.

Contribution

It clarifies the relationship between UV theory properties and the sign of K"ahler potential terms using unitarity arguments, with examples from supersymmetric gauge theories and string models.

Findings

Unitarity constrains the sign of quartic K"ahler terms.

Examples include large N supersymmetric gauge theories.

Implications for inflationary and SUSY-breaking models.

Abstract

In supersymmetric theories, the signs of quartic terms in the K\"ahler potential control the stability of non-supersymmetric field configurations. In particular, in supersymmetric inflation models, the signs are important for the stability of an inflationary trajectory as well as for the prediction of the spectral index. In this paper, we clarify what properties of a UV theory determine the sign from unitarity arguments of scattering amplitudes. As non-trivial examples, we discuss the sign of a four-meson term in large $N$ supersymmetric gauge theories and also those of the quartic terms obtained in the intersecting D-brane models in superstring theory. The UV origins of inflationary models and supersymmetry breaking models are constrained by this discussion.