On parity-odd sector in metric-affine theories

Abstract

We undertake the construction of quadratic parity-violating terms involving the curvature in the four-dimensional metric-affine gravity. We demonstrate that there are only 12 linearly independent scalars, plus an additional one that can be removed by using the Pontryagin invariant. Several convenient bases for this sector are provided in both components and differential form notation. We also particularize our general findings to some constrained geometries like Weyl-Cartan and metric-compatible connections.

12 pages, no figures, no tables. Added: small changes and some references. Version to be published in EPJC

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Cited by in corpus (3)

• Landau damping for gravitational waves in parity-violating theories
• Hamiltonian analysis of metric-affine-$R^2$ theory
• Does the metric play a fundamental role in the building of gravitational models?