37 lines
1.4 KiB
Text
37 lines
1.4 KiB
Text
/-
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Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Joseph Tooby-Smith
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-/
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import HepLean.BeyondTheStandardModel.PatiSalam.Basic
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import HepLean.Meta.Informal
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/-!
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# The Spin(10) Model
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Note: By physicists this is usually called SO(10). However, the true gauge group involved
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is Spin(10).
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-/
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namespace Spin10Model
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informal_definition GaugeGroupI where
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math :≈ "The group `Spin(10)`."
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physics :≈ "The gauge group of the Spin(10) model (aka SO(10)-model.)"
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informal_definition inclPatiSalam where
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physics :≈ "The inclusion of the Pati-Salam gauge group into Spin(10)."
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math :≈ "The lift of the embedding `SO(6) x SO(4) → SO(10)` to universal covers,
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giving a homomorphism `Spin(6) x Spin(4) → Spin(10)`. Precomposed with the isomorphism,
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``PatiSalam.gaugeGroupISpinEquiv, between `SU(4) x SU(2) x SU(2)` and `Spin(6) x Spin(4)`."
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ref :≈ "Page 56 of https://math.ucr.edu/home/baez/guts.pdf"
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deps :≈ [``GaugeGroupI, ``PatiSalam.GaugeGroupI, ``PatiSalam.gaugeGroupISpinEquiv]
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informal_definition inclSM where
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physics :≈ "The inclusion of the Standard Model gauge group into Spin(10)."
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math :≈ "The compoisiton of ``embedPatiSalam and ``PatiSalam.inclSM."
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ref :≈ "Page 56 of https://math.ucr.edu/home/baez/guts.pdf"
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deps :≈ [``inclPatiSalam, ``PatiSalam.inclSM]
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end Spin10Model
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