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

Abstract The Grassmann envelope is used to find the 𝒩 = 1 ‘superquasiconformal’ algebra in D = 10 + 1. The adjoint representation of this algebra is found to contain 𝔰𝔲 2,2 ⊕ u 1 ⊕ 𝔰𝔲 5 as a submaximal subalgebra, giving a spectrum of conformal gravity with flipped SU 5 × 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.