Chiral Asymmetry and the Spectral Action

TL;DR

This paper computes the spectral action for various Dirac operators on manifolds with torsion, revealing connections to quantum gravity, the Standard Model, and predicting the Barbero-Immirzi parameter.

Contribution

It introduces explicit spectral action calculations for Dirac operators with torsion, linking geometric, quantum gravity, and particle physics concepts.

Findings

Derivation of the Holst term from spectral action

Coupling of Holst term to scalar curvature

Prediction of the Barbero-Immirzi parameter value

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.