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

TL;DR

This paper constructs a unified model combining flipped $SU(5)$ GUT with conformal gravity using a single supermultiplet, leading to a novel action that includes gravity, GUT gauge bosons, fermions, and a Higgs sector without superpartners.

Contribution

It introduces a superalgebra framework that unifies conformal gravity and flipped $SU(5)$ GUT within a single supermultiplet, avoiding superpartners and incorporating multiple particle sectors.

Findings

Derivation of a superquasiconformal algebra in 11D

Spectrum includes conformal gravity with flipped $SU(5) imes U(1)$

An explicit action combining gravity, GUT, fermions, and Higgs sectors

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.