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Orbifold GUTs

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Supersymmetric Grand Unified Theories

Part of the book series: Lecture Notes in Physics ((LNP,volume 939))

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Abstract

Let us briefly review the geometric picture of GUT models compactified on a circle S1. The circle \(S^{1} \equiv \mathbb{R}^{1}/\mathcal{T}\) where \(\mathcal{T}\) is the action of translations by 2π R. All fields Φ are thus periodic functions of the fifth dimension x 5 = y with \(\varPhi (x_{\mu },y) \rightarrow \varPhi (x_{\mu },y + 2\pi R) =\varPhi (x_{\mu },y)\) (see Fig. 14.1).

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Notes

  1. 1.

    In [291] we constructed ’t Hooft–Polyakov monopole strings in the 5D orbifold GUT theory.

  2. 2.

    Recall, for a background field gauge with A M  = A M cl + a M where A M cl is the background value of the gauge field and a M are the small fluctuations, the background covariant derivative is given by D M cl ≡ ∂ M + i[A M cl,   ]. If we use the covariant gauge fixing condition D M cl a M  ≡ 0, then the gauge field equations of motion are given by D M cl D M cl a N + 3iF NM cl a M = 0. Note, for a constant background gauge field F NM cl ≡ 0.

  3. 3.

    See problem 10.

  4. 4.

    Where it is assumed that [P, T] = 0.

  5. 5.

    Note, \(A_{5}^{3}(-y) = -A_{5}^{3}(y) + \frac{1} {R}\).

  6. 6.

    The 5D \(\gamma _{5} = i\left (\begin{array}{cc} - \mathbb{I}_{2\times 2} & 0 \\ 0 & \mathbb{I}_{2\times 2} \end{array} \right )\).

  7. 7.

    See problem 11.

  8. 8.

    For other orbifold GUT models in 5D, see [298, 303, 305, 315–318] or 6D, see [319, 320].

  9. 9.

    See problem 12.

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  1. Department of Physics, The Ohio State University, Columbus, Ohio, USA

    Stuart Raby

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Raby, S. (2017). Orbifold GUTs. In: Supersymmetric Grand Unified Theories. Lecture Notes in Physics, vol 939. Springer, Cham. https://doi.org/10.1007/978-3-319-55255-2_14

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