Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

Details Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

2006-04-11

arxiv.org/abs/hep-th/0604084v2

JHEP0606:038,2006

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, no figure

Scientific paper

10.1088/1126-6708/2006/06/038

In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space.

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