Gauging the superconformal group with a graded dual operator

Abstract

Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is gauge invariant under the grading even bosonic generators. We provide a self-dual notion based on the dual operator. We use the definition of the dual operator to contruct a model with gauge invariance $SO(1,3)\times SU(N)\times U(1)\subset SU(2,2|N)$. The choice of a graded dual operator allows us to overcome technical difficulties of $U(N)$ unified theories based on the superconformal group. The gravity action reproduces the Einstein-Hilbert action in certain sector of the theory. The definition of the dual operator allows us to include fermionic matter in the gauge connection in a geometric manner. We give a summary with possible phenomenological parameters that are included in the model.

References in corpus (3)

• Dynamical systems with benign ghosts
• Chiral gauge theory and gravity from unconventional supersymmetry
• $\mathcal{N}=2$ Extended MacDowell-Mansouri Supergravity

Cited by in corpus (5)

• A black hole solution in conformal supergravity
• Self duality in unconventional conformal supersymmetry
• Embedding of the Georgi-Glashow $SU(5)$ model in the superconformal algebra
• Embedding of rank two supercharges in the superconformal algebra
• Spinor solutions of a Chern-Simons model for the superconformal algebra