https://doi.org/10.1140/epjc/s10052-023-11250-2
Regular Article - Theoretical Physics
On parity-odd sector in metric-affine theories
1
Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, 37008, Salamanca, Spain
2
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411, Tartu, Estonia
3
Russian Academy of Sciences, Nuclear Safety Institute, B.Tulskaya 52, 115191, Moscow, Russia
b
alejandro.jimenez.cano@ut.ee
Received:
22
November
2022
Accepted:
22
January
2023
Published online:
3
February
2023
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.
© The Author(s) 2023
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