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Can metric-affine gravity be saved?

Will Barker, Carlo Marzo, Alessandro Santoni

TL;DR

The paper investigates whether metric-affine gravity (MAG) can be a viable effective quantum theory by enforcing a symmetry-first approach within an effective field theory (EFT) framework. It argues that, to avoid ghosts and tachyons, additional symmetries beyond diffeomorphism invariance are essential, and then systematically searches for symmetry realizations compatible with a parity-preserving, totally symmetric distortion. The authors find that such a framework allows only massless spin-1 and spin-3 modes in the flat limit (besides the graviton), with scalar-generated symmetries failing to yield viable models and tensor generators providing consistent, radiatively stable structures—most notably recovering a Fronsdal spin-3 sector in one branch. The work emphasizes that the healthy MAG foundations are obtained without arbitrary coupling tuning, guiding future exploration toward full MAG with relaxed symmetry restrictions and potential mass generation via compensator fields or non-perturbative effects. Overall, the study strengthens the case for constructing MAG as a controlled EFT whose IR foundations are dictated by symmetry and consistency conditions rather than geometric heuristics alone.

Abstract

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.

Can metric-affine gravity be saved?

TL;DR

The paper investigates whether metric-affine gravity (MAG) can be a viable effective quantum theory by enforcing a symmetry-first approach within an effective field theory (EFT) framework. It argues that, to avoid ghosts and tachyons, additional symmetries beyond diffeomorphism invariance are essential, and then systematically searches for symmetry realizations compatible with a parity-preserving, totally symmetric distortion. The authors find that such a framework allows only massless spin-1 and spin-3 modes in the flat limit (besides the graviton), with scalar-generated symmetries failing to yield viable models and tensor generators providing consistent, radiatively stable structures—most notably recovering a Fronsdal spin-3 sector in one branch. The work emphasizes that the healthy MAG foundations are obtained without arbitrary coupling tuning, guiding future exploration toward full MAG with relaxed symmetry restrictions and potential mass generation via compensator fields or non-perturbative effects. Overall, the study strengthens the case for constructing MAG as a controlled EFT whose IR foundations are dictated by symmetry and consistency conditions rather than geometric heuristics alone.

Abstract

Like general relativity, metric-affine gravity should be a viable effective quantum theory, otherwise it is a mathematical curiosity without physical application. Assuming a perturbative quantum field theory, the universal, flat limit of metric-affine gravity offers a good foundation for model-building only when symmetry constraints are themselves sufficient to get rid of ghosts and tachyons in the spectrum of propagating particle states, without requiring any further tuning of the couplings. Using this symmetry-first criterion, we find that for parity-preserving models with a totally symmetric distortion, only massless spin-one and spin-three modes are possible besides the graviton. Moreover, no viable models result from gauge symmetries generated by a scalar field.

Paper Structure

This paper contains 2 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Effective field theory

Figures (2)

  • Figure 1: From \ref{['MAGFDef']} curvature $\MAGF{_{\mu\nu}^\rho_\sigma}$ rotates a vector after parallel transport around a closed loop. From \ref{['MAGTDef']} torsion $\MAGT{_\mu^\alpha_\nu}$ causes non-closure of parallelograms formed from (infinitesimally) parallel-transported vectors. From \ref{['MAGQDef']} non-metricity $\MAGQ{_{\lambda\mu\nu}}$ causes the evolution of vector length (norm) under parallel transport.
  • Figure 2: Ghost-tachyon-free metric-affine gravity (MAG) Lagrangians are normally made from tuned admixtures of the scalar invariants of the geometric tensors illustrated in \ref{['NonRiemannianSchematic']}. Such theories will 'de-tune' at the loop level, unless protected by symmetries beyond $\DiffeomorphismGroup{}$ diffeomorphism invariance.