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Scalar and spinor field actions on fuzzy S 4: fuzzy \(\mathbb{C}{{\text{P}}^3}\) as a \(S_F^2\) bundle over \(S_F^4\)

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Abstract

We present a manifestly Spin(5) invariant construction of squashed fuzzy \(\mathbb{C}{{\text{P}}^3}\) as a fuzzy S 2 bundle over fuzzy S 4. We develop the necessary projectors and exhibit the squashing in terms of the radii of the S 2 and S 4. Our analysis allows us give both scalar and spinor fuzzy action functionals whose low lying modes are truncated versions of those of a commutative S 4.

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Authors and Affiliations

  1. Ciencias Básicas (UPIITA), Instituto Politécnico Nacional (IPN), Av. IPN 2580, Col. La Laguna Ticomán, 07340, México, D.F., Mexico

    Julieta Medina

  2. Theoretisch-Physikalisches Institut, Friedrich-Schiller Universität, Jena, Max-Wien-Platz 1, D-07743, Thüringen, Germany

    Idrish Huet

  3. School of Theoretical Physics, Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin 4, Ireland

    Denjoe O’Connor & Brian P. Dolan

  4. Department of Mathematical Physics, National University of Ireland (NUI) Maynooth, Maynooth Co., Kildare, Ireland

    Brian P. Dolan

Authors
  1. Julieta Medina
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  2. Idrish Huet
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  3. Denjoe O’Connor
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  4. Brian P. Dolan
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Correspondence to Idrish Huet.

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ArXiv ePrint: 1208.0348

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Medina, J., Huet, I., O’Connor, D. et al. Scalar and spinor field actions on fuzzy S 4: fuzzy \(\mathbb{C}{{\text{P}}^3}\) as a \(S_F^2\) bundle over \(S_F^4\) . J. High Energ. Phys. 2012, 70 (2012). https://doi.org/10.1007/JHEP08(2012)070

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