Geometry and unitarity of scalar fields coupled to gravity

Author:

Minxi He, Kohei Kamada, Kyohei Mukaida

Keyword:

High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), Cosmology and Nongalactic Astrophysics (astro-ph.CO), High Energy Physics - Theory (hep-th)

journal:

KEK-TH-2547, KEK-Cosmo-0320, RESCEU-19/23

date:

2023-08-28 16:00:00

Abstract

We formulate scalar field theories coupled non-conformally to gravity in a manifestly frame-independent fashion. Physical quantities such as the $S$-matrix should be invariant under field redefinitions, and hence are represented by the geometry of the target space. This elegant geometric formulation, however, is obscured when considering the coupling to gravity because of the redundancy associated with the Weyl transformation. The well-known example is the Higgs inflation, where the target space of Higgs is flat in the Jordan frame but is curved in the Einstein frame. Furthermore, one can even show that any geometry of O$(N)$ nonlinear $\sigma$ models can be flattened by an appropriate Weyl transformation. In this letter, we extend the notion of the target space by including the conformal mode of the metric, and show that the extended geometry provides a compact formulation that is manifestly Weyl-transformation/field-redefinition invariant. We estimate the scale of the perturbative unitarity violation from the two-to-two scattering amplitudes based on this formalism.

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