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

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 $S{U}_5\times U_1$ 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.

9 pages. Contribution to the Proceedings of the 28th International Conference on Integrable Systems and Quantum Symmetries (ISQS-28), Prague, Czechia, July 1-5, 2024