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Finite quantum field theories: Clifford algebras for Yukawa couplings?

Wolfgang Lucha·Michael Moser
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Abstract

By imposing on the most general renormalizable quantum field theory the requirement of the absence of ultraviolet-divergent renormalizations of the physical parameters (masses and coupling constants) of the theory, finite quantum field theories in four space-time dimensions may be constructed. Famous prototypes of these form certain well-known classes of supersymmetric finite quantum field theories. Within a perturbative evaluation of the quantum field theories under consideration, the starting point of all such investigations is represented by the conditions for one- and two-loop finiteness of the gauge couplings as well as for one-loop finiteness of the Yukawa couplings. Particularly attractive solutions of the one-loop Yukawa finiteness condition involve Yukawa couplings which are equivalent to generators of Clifford algebras with identity element. However, a closer inspection shows, at least for all simple gauge groups up to and including rank 8, that these Clifford-like solutions prove to be inconsistent with the requirements of one- and two-loop finiteness of the gauge coupling and of absence of gauge anomalies.

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Wolfgang Lucha, Michael Moser. 1997-10-27. Finite quantum field theories: Clifford algebras for Yukawa couplings?. https://arxiv.org/abs/hep-th/9710202

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