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Anomaly-mediated scalar gravitational interactions and the coupling of conformal sectors

Claudio Corianò1,2, Stefano Lionetti1, Dario Melle1, and Leonardo Torcellini1

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Phys. Rev. D 114, 044034 – Published 11 August, 2026

DOI: https://doi.org/10.1103/pmr2-b6qq

Abstract

We investigate the anomaly-induced activation of a gauge-invariant scalar degree of freedom in general relativity, the conformalon mode, directly at the level of 2→2 scattering amplitudes. The analysis couples anomalous three-point functions of conformal sectors, involving gravitons (TTT) and Abelian gauge currents (TJJ), through single-graviton exchange derived from the quadratic expansion of the Einstein-Hilbert action. Unlike related treatments based on the nonlocal anomaly action, these interactions are suppressed by the Planck scale. We show that the conformalon, invariant under linearized diffeomorphisms, admits an interpretation as an effective scalar correction to scattering amplitudes, both in virtual exchange channels and in effective real-emission processes. Around flat space, this behavior arises from anomaly-induced nonlocal massless insertions on the external graviton and photon legs of the three-point functions, sewn through the scalar component of the graviton propagator in De Donder gauge. The resulting anomaly-mediated four-point interaction reduces to contact terms, with the Planck mass setting the suppression scale. The construction consistently matches the spin decomposition of flat-space conformal Ward identities in momentum space, which determine the vertices, with the corresponding spin decomposition of the graviton propagator. In the eikonal limit, these interactions generate contact corrections to the leading logarithmic phase in impact-parameter space. We further show that anomaly-mediated 2→2 graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

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Phys. Rev. D 114, 044034– Published 11 August, 2026
  • Received 13 April 2026
  • Accepted 10 July 2026
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