Chiral Asymmetry and the Spectral Action

Abstract

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.

References in corpus (7)

• Beyond Einstein-Cartan gravity: Quadratic torsion and curvature invariants with even and odd parity including all boundary terms
• Noncommutative Geometry as a Framework for Unification of all Fundamental Interactions including Gravity. Part I
• Poincare gauge theory of gravity: Friedman cosmology with even and odd parity modes. Analytic part
• Spectral action for torsion with and without boundaries
• The Holst Action by the Spectral Action Principle
• Spectral action for scalar perturbations of Dirac operators
• A relation between the Barbero-Immirzi parameter and the standard model

Cited by in corpus (6)

• Dirac Operators with Torsion and the Noncommutative Residue for Manifolds with Boundary
• A Kastler-Kalau-Walze Type Theorem for 5-dimensional Manifolds with Boundary
• Dirac operators with torsion, spectral Einstein functionals and the noncommutative residue
• A Dark Sector Extension of the Almost-Commutative Standard Model
• Spectral forms and de-Rham Hodge operator
• The spectral torsion for the Connes type operator