Actions for twisted spectral triple and the transition from the Euclidean to the Lorentzian

This is a review of recent results regarding the application of Connes' noncommutative geometry to the Standard Model, and beyond. By twisting (in the sense of Connes-Moscovici) the spectral triple of the Standard Model, one does not only get an extra scalar field which stabilises the electroweak vacuum, but also an unexpected 1-form field. By computing the fermionic action, we show how this field induces a transition from the Euclidean to the Lorentzian signature. Hints on a twisted version of the spectral action are also briefly mentioned.