Speaker
Description
Noncommutative/quantum geometry is the program of studying geometry on noncommutative algebras (modeling quantum coordinates and spacetime functions) endowed with some extra structure (Dirac operator and Hilbert space) giving rise to a spectral triple. It is well known that a special noncommutative geometry, via the spectral action principle, uniquely leads to the classical Standard Model Lagrangian, with all of the correct field representations and symmetry breaking mechanism, coupled to gravity (and optionally right handed Majorana neutrinos).
This internal noncommutative geometry can be viewed as the product of smooth spacetime manifold with a finite internal space. Recently in [1] it was shown that this internal quantum geometry behind the Standard Model definitely carries nonzero torsion tensor and that its components are proportional to the Yukawa couplings. Additionally, Ricci (scalar and tensor) curvatures, along with the Einstein tensor, were computed for this internal geometry and it was found that the results depend on the Majorana mass matrix $\Upsilon_R$, offering perhaps a quantum-geometric test of the existence of Majorana neutrinos and their mass.
[1] - L. Dabrowski, S. Mukhopadhyay and F. Pozar, Spectral torsion of the internal noncommutative geometry of the Standard Model,
[arXiv:2511.08159 [hep-th]].