Parity Violating Metric-Affine Gravity Theories

TL;DR

This paper investigates a parity-violating Metric-Affine gravity theory with the Holst term, demonstrating its equivalence to general relativity under certain conditions and exploring extensions to f(R) models and matter coupling.

Contribution

It shows that the Holst term leads to invariance and equivalence to GR in vacuum, and extends the analysis to f(R) gravity and matter interactions.

Findings

For a specific Barbero-Immirzi parameter, the action is invariant under certain connection transformations.

In all cases, the connection reduces to Levi-Civita with appropriate gauge choices, making the theory equivalent to GR in vacuum.

f(R) models with non-constant derivatives are on-shell equivalent to scalar-tensor theories.

Abstract

We study a parity violating Metric-Affine gravitational theory given by the Einstein-Hilbert action plus the so-called Holst term in vacuum. We find out that for a certain value of the Barbero-Immirzi parameter the total action possesses a remarkable invariance under particular transformations of the affine connection. We prove that in all cases, with appropriate gauge choices, the connection reduces to the Levi-Civita one and that the theory turns out to be equivalent to general relativity in vacuum. Subsequently, we generalize our discussion and analyze the case of Metric-Affine $f(R)$ gravity plus the Holst term. In particular, we show that for $f'(R) \neq \text{constant}$ the theory results to be on-shell equivalent to a metric-compatible torsionless Scalar-Tensor model. Matter coupling of the aforementioned models is also discussed, together with explicit examples and applications.