{\cal N}=1$ supersymmetry in $4D$ gravity with torsion and non-metricity
We study the inclusion of fermionic degrees of freedom and ${\cal N}=1$ supersymmetry in 4-dimensional manifolds with arbitrary torsion and non-metricity tensors deforming the connection. We inspect the closure of local diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and g...
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Zusammenfassung: | We study the inclusion of fermionic degrees of freedom and ${\cal N}=1$
supersymmetry in 4-dimensional manifolds with arbitrary torsion and
non-metricity tensors deforming the connection. We inspect the closure of local
diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and
gravitino at leading order in fermions. The closure of a pair of supersymmetric
transformations acting on the vielbein restricts the form of the spin
connection. The dependency of the latter on the fundamental fields is
exclusively given by the vielbein, up to Lorentz and/or diffeomorphisms
brackets, independently of the torsion or non-metricity deformations of the
affine connection, which is not restricted by supersymmetry at this order. We
have then studied the couple of the Rarita-Schwinger theory to a generic
gravitational Lagrangian; the supersymmetric variation of the former restricts
the form of the bosonic Lagrangian in order to accomplish invariance. Special
cases where $R_{\mu \nu}{}^{ab}=0$, $Q_{\mu \nu \rho}=0$ or $T_{\mu
\nu}{}^{\rho}=0$ are provided. |
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DOI: | 10.48550/arxiv.2207.12466 |