Unification based on SO*(14) Yang-Mills theory: the gauge field Lagrangian

Abstract

Gravity can be described as a gauge field theory where connection and curvature are so(2,3) valued. In the standard gauge field theory for strong and electroweak interactions, corresponding quantities take their value in the su(3)(+)su(2)(+)u(1) algebra. Therefore, unification of gravity with the other fundamental interactions is obtained by using the non-compact simple real Lie algebra so(14) contains/implies so(2,3)(+)su(3)(+)su(2)(+)u(1) as a unifying algebra. Commutation relations for so*(14) are derived in a basis adapted to this subalgebra structure. The so*(14) gauge field defined by a connection one-form on the SO*(14) principal fibre bundle unifies the fundamental interactions in particle physics, gravity included. The 91 components of the connection contain the 10 anti-de Sitter gauge fields, the 12 gauge bosons associated with SU(3)(+)SU(2)(+)U(1), two SU(3) triplets of lepto-quark bosons. An anti-de Sitter five-vector which is also an SU(2) triplet and finally two SU(3) triplets of four-spinors which are also SU(2) doublets. Although so*(14) is a Lie algebra and not a superalgebra, it is a general property of the theory that bosons and fermions can be incorporated in irreducible supermultiplets. The unified gauge field Lagrangian is defined by the Yang-Mills Weil form on the SO*(14) principal bundle.