On twisting real spectral triples by algebra automorphisms

Abstract

We systematically investigate ways to twist a real spectral triple via an algebra automorphism and in particular, we naturally define a twisted partner for any real graded spectral triple. Among other things we investigate consequences of the twisting on the fluctuations of the metric and possible applications to the spectral approach to the standard model of particle physics.

References updated, minor corrections, result on the unicity of the minimal twist for manifolds strengthened

References in corpus (3)

• Resilience of the Spectral Standard Model
• Type III and spectral triples
• On the Chern-Gauss-Bonnet Theorem and Conformally Twisted Spectral Triples for $C^{\ast }$-Dynamical Systems

Cited by in corpus (12)

• Lorentz signature and twisted spectral triples
• A survey of spectral models of gravity coupled to matter
• Gauge transformations for twisted spectral triples
• A spectral geometry for the Standard Model without the fermion doubling
• Spectral Action in Noncommutative Geometry
• Twisted Standard Model in noncommutative geometry I: the field content
• On twisted reality conditions
• Lorentzian fermionic action by twisting euclidean spectral triples
• Twisted Spectral Triples without the First-Order Condition
• Twisting Noncommutative Geometries with Applications to High Energy Physics
• Real Part of Twisted-by-Grading Spectral Triples
• A critical survey of twisted spectral triples beyond the Standard Model