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Chiral Asymmetry and the Spectral Action

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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.

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Authors and Affiliations

  1. Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3-5, Göttingen, Germany

    Frank Pfäffle

  2. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, Bonn, Germany

    Frank Pfäffle

  3. Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, Hamburg, Germany

    Christoph A. Stephan

  4. Institut für Mathematik, Universität Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Christoph A. Stephan

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  1. Frank Pfäffle
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  2. Christoph A. Stephan
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Correspondence to Christoph A. Stephan.

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Communicated by A. Connes

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Pfäffle, F., Stephan, C.A. Chiral Asymmetry and the Spectral Action. Commun. Math. Phys. 321, 283–310 (2013). https://doi.org/10.1007/s00220-012-1641-6

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