# Conformally covariant operators of mixed-symmetry tensors and MAGs

## TL;DR

This paper classifies conformally covariant operators for mixed-symmetry tensors in arbitrary dimensions, enabling the formulation of conformal actions in metric-affine gravity theories with torsion and nonmetricity.

## Contribution

It completes the classification of quadratic conformal actions for tensors with three indices and extends this to all tensor species in metric-affine gravity.

## Key findings

- Derived conformally covariant actions for mixed-symmetry tensors.
- Classified all quadratic conformal actions for tensors with three indices.
- Discussed propagating degrees of freedom and interacting theories.

## Abstract

We compute conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension $d$. Our results complete the classification of conformal actions that are quadratic on arbitrary tensors with three indices, which allows to write corresponding conformal actions for all tensor species that appear in the decomposition of the distorsion tensor of an arbitrary metric-affine theory of gravity including both torsion and nonmetricity. We also discuss the degrees of freedom that such theories are propagating, as well as interacting metric-affine theories that enjoy the conformal actions in the Gaussian limit.