\( \mathcal{N} = 2\) extended Macdowell-Mansouri supergravity

DOI10.1007/JHEP07(2021)176zbMATH Open1468.83053arXiv2105.14606OpenAlexW3211285127MaRDI QIDQ1981536

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Publication date: 3 September 2021

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Abstract: We construct a gauge theory based in the supergroup $G=SU(2,2|2)$ that generalizes MacDowell-Mansouri supergravity. This is done introducing an extended notion of Hodge operator in the form of an outer automorphism of $su(2,2|2)$-valued 2-form tensors. The model closely resembles a Yang-Mills theory -- including the action principle, equations of motion and gauge transformations -- which avoids the use of the otherwise complicated component formalism. The theory enjoys $H=SO(3,1)imesmathbbRimesU(1)imesSU(2)$ off-shell symmetry whilst the broken symmetries $G/H$, translation-type symmetries and supersymmetry, can be recovered on surface of integrability conditions of the equations of motion, for which it suffices the Rarita-Schwinger equation and torsion-like constraints to hold. Using the extit{matter ansatz} -- projecting the $1otimes1/2$ reducible representation into the spin-$1/2$ irreducible sector -- we obtain (chiral) fermion models with gauge and gravity interactions.

Full work available at URL: https://arxiv.org/abs/2105.14606

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