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arXiv · 2412.20191

Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet

David Chester·Alessio Marrani·Michael Rios·Klee Irwin
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Abstract

The Grassmann envelope is used to find the $\mathcal{N}=1$ `superquasiconformal' algebra in $D=10+1$. The adjoint representation of this algebra is found to contain $\mathfrak{su}_{2,2}\oplus \mathfrak{u}_{1}\oplus \mathfrak{su}_{5}$ as a submaximal subalgebra, giving a spectrum of conformal gravity with flipped $SU_{5}\times U_{1}$ GUT. Combining Yang-Mills theory with MacDowell-Mansouri gravity over the conformal group is found to recover the Einstein-Hilbert action with a cosmological constant. An action for the theory is presented, which contains the gauge bosons of gravity and GUT, three generations of fermions in an efficient manner, and a new Higgs sector. By using the superalgebra for the entire multiplet, the theory gauges a non-supersymmetric subalgebra without introducing superpartners.

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David Chester, Alessio Marrani, Michael Rios, Klee Irwin. 2024-12-28. Flipped $SU(5)$ GUT with conformal gravity from a single supermultiplet. https://doi.org/10.1088/1742-6596/2912/1/012040

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