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

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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http://hal.in2p3.fr/in2p3-00125040
Contributor : Dominique Girod <>
Submitted on : Wednesday, January 17, 2007 - 3:09:24 PM
Last modification on : Tuesday, November 19, 2019 - 9:08:02 PM

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J. Thierry-Mieg. Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra. Journal of High Energy Physics, Springer, 2006, 06, pp.038. ⟨10.1088/1126-6708/2006/06/038⟩. ⟨in2p3-00125040⟩

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