$\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity
| Autor: | Alvarez, Pedro D., Delage, Lucas, Valenzuela, Mauricio, Zanelli, Jorge |
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| Rok vydání: | 2021 |
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| Zdroj: | JHEP 07 (2021) 176 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/JHEP07(2021)176 |
| Popis: | 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 $H=SO(3,1)\times \mathbb{R} \times U(1)\times SU(2)$ 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 \textit{matter ansatz} -- projecting the $1 \otimes 1/2$ reducible representation into the spin-$1/2$ irreducible sector -- we obtain (chiral) fermion models with gauge and gravity interactions. Comment: 34 pages. References added in the second version. Published |
| Databáze: | arXiv |
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