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Spectral Action for Torsion with and without Boundaries

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Abstract

We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter θ of the boundary conditions, and show that θ = 0 is a critical point of the action in any dimension and at all orders of the expansion.

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Authors and Affiliations

  1. UMR 6207, Centre de Physique Théorique, CNRS-luminy, Case 907, 13288, Marseille Cedex 9, France

    B. Iochum

  2. Université de Provence, Marseille, France

    B. Iochum

  3. Department of Mathematical Sciences, University of Copenhagen, Copenhagen, Denmark

    C. Levy

  4. CMCC– Universidade Federal do ABC, Santo André, S.P., Brazil

    D. Vassilevich

  5. Department of Theoretical Physics, St. Petersburg University, St. Petersburg, Russia

    D. Vassilevich

Authors
  1. B. Iochum
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  2. C. Levy
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  3. D. Vassilevich
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Correspondence to B. Iochum.

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Communicated by A. Connes

UMR 6207: Unité Mixte de Recherche du CNRS et des Universités Aix-Marseille I, Aix-Marseille II et de l’Université du Sud Toulon-Var (Aix-Marseille Université); Laboratoire affilié à la FRUMAM – FR 2291.

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Iochum, B., Levy, C. & Vassilevich, D. Spectral Action for Torsion with and without Boundaries. Commun. Math. Phys. 310, 367–382 (2012). https://doi.org/10.1007/s00220-011-1406-7

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  • DOI: https://doi.org/10.1007/s00220-011-1406-7

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