Day 3: a summary


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This morning (Wednesday 16 October) Ali Chamseddine lectured on what NCG can say about the SM and Beyond. In particular, he explained that the dropping of the mathematical condition of being at first-order in the noncommutative derivation of the Standard Model naturally leads to Pati-Salam SU(2) × SU(2) × SU(4) Grand Unified Theory. Besides all Standard Model fermions being in the right representation, there are additional scalar fields in the right representation to allow for a truncation to the Standard Model, including the σ-field that allowed for a realistic Higgs mass. Next, Enrique Alvarez gave an interesting seminar about unimodular gravity, containing an interesting discussion on the conformal anomaly.

Because of mutual interest, during the afternoon the studygroups ‘Higgs vacuum stability‘ and ‘Lorentzian NCG‘ were promoted to two elucidating plenary discussions. Among other topics, in the first the origin and significance of the aforementioned σ-field was discussed. In the second discussion session a proposal was put forward to induce the spectral Standard Model via the determinant of the (noncommutative) Dirac operator, i.e. the fermionic partition function. This might be suitable for a generalization of the spectral action to Lorentzian NCG, even though the actual computation of the path integral then still demands for a Wick rotation of the Dirac operator to Euclidean signature.

After this inspiring day of lectures and discussions, a boat trip excursion was awaiting us, as well as the conference dinner on board.

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