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arXiv · hep-th/0604084

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

Jean Thierry-Mieg
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Abstract

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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Jean Thierry-Mieg. 2006-04-11. Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra. https://doi.org/10.1088/1126-6708%2F2006%2F06%2F038

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