On the Gravitational Origin of the QCD Axion

TL;DR

This paper investigates the potential of gravity-induced scalar fields, especially in Weyl-invariant Einstein-Cartan gravity, to serve as axions solving the strong CP problem, and discusses the conditions needed for their viability.

Contribution

It critically assesses gravitational axion models, identifies limitations of derivative couplings, and highlights Weyl-invariant Einstein-Cartan gravity as a promising framework.

Findings

Derivative coupling models do not produce satisfactory axions.

Weyl-invariant Einstein-Cartan gravity can generate gravitational axions.

Quantum effects are crucial for gravitational axion generation.

Abstract

Gravity can give rise to (pseudo)scalar fields, for instance due to torsion. In particular, axions of gravitational origin have been proposed as a minimal and compelling solution to the strong CP problem. In this work, we critically examine the feasibility of this approach. We demonstrate that models in which the scalar field couples to fermionic currents only through derivatives do not yield a satisfactory axion. Moreover, we identify the necessary conditions for generating a gravitational axion through quantum effects, highlighting Weyl-invariant Einstein-Cartan gravity as a promising theoretical setting.