Infra-red enhanced loops in quadratic gravity

TL;DR

This paper investigates the nature of infra-red loop corrections in quadratic gravity, revealing their gauge dependence and process-specific effects, and clarifies the role of ghosts in the effective action.

Contribution

It demonstrates that infra-red loop corrections in quadratic gravity are gauge-dependent and process-specific, challenging the interpretation of these effects as physical running couplings.

Findings

Infra-red log-enhanced corrections are gauge and parameterisation dependent.

Genuine infra-red corrections are process-dependent and cannot be absorbed into couplings.

The ghost in quadratic gravity does not affect the positivity bounds of the effective action.

Abstract

It has been suggested that logarithmically enhanced infra-red loop corrections arising in theories with four derivatives correspond to a physical running of couplings, rendering quadratic gravity asymptotically free. We find that these effects depend on the gauge and on the field parameterisation. We compute physical on-shell amplitudes and find genuine infra-red log-enhanced loop corrections, that are process-dependent and cannot be absorbed into running couplings. As a byproduct, we derive the effective action of quadratic gravity at tree level, showing that its ghost does not contribute to effective operators and thereby does not violate positivity bounds.