# Different types of torsion and their effect on the dynamics of fields

## TL;DR

This paper explores how different types of torsion in gravity, especially within the vierbein-Einstein-Palatini formalism, influence the dynamics of fields, revealing non-uniqueness in conformal transformations and effects on fermions and scalar fields.

## Contribution

It analyzes the conformal properties of torsion and spin connection in the VEP formalism, identifying conditions leading to Nieh-Yan theory and conformally invariant torsion.

## Key findings

- Conformal transformation of off-shell spin connection is not unique without extra assumptions.
- Dynamically generated torsion affects the conformal properties of the spin connection.
- Torsion influences the dynamics of fermions and non-minimally coupled scalar fields.

## Abstract

One of the formalisms that introduces torsion conveniently in gravity is the vierbein-Einstein-Palatini (VEP) formalism. The independent variables are the vierbein (tetrads) and the components of the spin connection. The latter can be eliminated in favor of the tetrads using the equations of motion in the absence of fermions; otherwise there is an effect of torsion on the dynamics of fields. We find that the conformal transformation of off-shell spin connection is not uniquely determined unless additional assumptions are made. One possibility gives rise to Nieh-Yan theory, another one to conformally invariant torsion; a one-parameter family of conformal transformations interpolates between the two. We also find that for dynamically generated torsion the spin connection does not have well defined conformal properties. In particular, it affects fermions and the non-minimally coupled conformal scalar field.