Abstract

In supersymmetric theories, the signs of quartic terms in the Kähler 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.

Highlights

  • In this paper, we study constraints on the sign of the quartic Kahler term from the unitarity arguments of the scattering amplitudes

  • As non-trivial examples, we discuss the sign of a four-meson term in large N supersymmetric gauge theories and those of the quartic terms obtained in the intersecting D-brane models in superstring theory

  • The quartic term in the Kahler potential modifies the shape of the scalar potential when supersymmetry is spontaneously broken

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Summary

Phenomenological motivations

The quartic term in the Kahler potential modifies the shape of the scalar potential when supersymmetry is spontaneously broken. In the context of inflation, the sign of the quartic Kahler term is important when it contains fields whose F -terms drive inflation, since such a term generates Hubble induced mass terms. It controls the curvature of the scalar manifold in two ways: (i) the curvature along the inflaton trajectory, which is related to the spectral index ns, and (ii) the stability of the orthogonal directions to the inflaton trajectory, are affected. The role of the quartic Kahler term has been discussed in ref. [39] in the context of modular inflation

UV theories and their effective theories
Amplitude analysis
Large N supersymmetric QCD
String theory amplitudes
Conclusion
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