Quantum Gravity and String Theory

   

On Octonionic Nonassociative Ternary Gauge Field Theories

Authors: Carlos Castro

A novel (to our knowledge) nonassociative Octonionic ternary gauge field theory is explicitly constructed based on a ternary-bracket structure involving the octonion algebra. The ternary bracket was defined earlier by Yamazaki. The antisymmetric rank-two field strength Fμν is defined in terms of the ternary-bracket (... see paper) involving an auxiliary octonionicvalued coupling (...) . The ternary bracket cannot be rewritten in terms of 2-brackets, [A,B,C] ≠ 1/4[[A,B],C]. It is found that gaugeinvariant matter kinetic terms for an octonionic-valued scalar field can be introduced in the action if one starts instead with an octonionic-valued rank-three antisymmetric field strength (...) permutations, which is defined in terms of an antisymmetric tensor field of rank two (...) and (...) We conclude with some preliminary steps towards the construction of generalized ternary gauge field theories involving both 3-Lie algebras and octonions.

Comments: 11 pages, submitted to Physics Letters B

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Submission history

[v1] 9 May 2011

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