Spectral action and the electroweak $\theta$-terms for the Standard Model without fermion doubling

Abstract

We compute the leading terms of the spectral action for a noncommutative geometry model that has no fermion doubling. The spectral triple describing it, which is chiral and allows for CP-symmetry breaking, has the Dirac operator that is not of the product type. Using Wick rotation we derive explicitly the Lagrangian of the model from the spectral action for a flat metric, demonstrating the appearance of the topological $\theta$-terms for the electroweak gauge fields.

26 pages

References in corpus (5)

• Resilience of the Spectral Standard Model
• The Electroweak Vacuum Angle
• Complex powers of the wave operator and the spectral action on Lorentzian scattering spaces
• Spectral Action in Noncommutative Geometry
• Suppression of Electroweak Instanton Processes in High-energy Collisions