Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Anomaly-mediated Scalar Gravitational Interactions and the Coupling of Conformal Sectors

Claudio Corianò, Stefano Lionetti, Dario Melle, Leonardo Torcellini

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 \(2\to2\) 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 behaviour 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 \(4\)-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 \(2\to2\) graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

Anomaly-mediated Scalar Gravitational Interactions and the Coupling of Conformal Sectors

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 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 behaviour 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 -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 graviton amplitudes associated with the virtual exchange of such modes exhibit a characteristic double-copy structure.

Paper Structure

This paper contains 39 sections, 391 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Scalar dilaton-like couplings to the anomaly
  3. The activation of extra modes in gravity
  4. Content of this work
  5. Sakharov's induced gravity for conformal and visible/dark sectors
  6. The anomaly and the nonlocal action: review
  7. The nonlocal action
  8. The $TJJ$ correlator and anomaly mediation
  9. The general conformal solution and its on-shell limit
  10. The perturbative implementation of the $TJJ$ correlator
  11. The anomaly
  12. Towards 4-point functions: spin projectors and the scalar sector in the de Donder gauge
  13. Spin decomposition of the graviton propagator
  14. Tree--level graviton exchange and the spin--0 channel in the De Donder gauge
  15. Scalar gravitational scattering and explicit breaking: the absence of scalar exchange in 4-point functions
  16. ...and 24 more sections

Figures (8)

  • Figure 1: $t$-channel scattering of two spin-1 states $p_1+p_2 \to p_3 + p_4$, mediated by the exchange of a single graviton (left). The two conformal sectors, represented by the darker blobs, may both belong to the visible sector or alternatively to one visible and one dark sector. The anomaly-mediated interaction between the two conformal sectors, responsible for the exchange of a scalar gravitational component, is shown on the right. This contribution arises from the combination of the external $R\Box^{-1}$ mixing with the spin-0 component of the graviton propagator.
  • Figure 2: Decomposition of the $TJJ$ vertex into an anomalous contribution and a transverse--traceless sector (black blob).
  • Figure 3: Spin-2 and spin-0 part of the graviton propagator.
  • Figure 4: The free field theory realization of the $TJJ$ vertex, here represented for an Abelian theory such as QED. The $J$ are coupled to photon lines (left). The mixing interaction induced by the graviton and the, corresponding in momentum space of a projector $\pi^{\mu\nu}$ on the external graviton line of any anomaly vertex (right).
  • Figure 5: $t$ and $s$ channel diagrams in the scattering of spin-1 with anomaly mediation.
  • ...and 3 more figures