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PhysLean.Particles.SuperSymmetry.SU5.ChargeSpectrum.ZMod

Charge spectra with values in ZMod n #

i. Overview #

The way that we have defined ChargeSpectrum means we can consider values of charges which are not only elements of ℤ, but also elements of other types.

In this file we will consider ChargeSpectrum which have values in ZMod n for various natural numbers n, as well as charge spectra with values in ZMod n × ZMod m.

In this file we focus on 4-insertions of singlets to be phenomenologically viable. In other files we usually just consider one.

ii. Key results #

iii. Table of contents #

iv. References #

There are no known references for the material in this module.

A. The finite set of viable ZMod n charge spectra #

A.1. General construction #

source
def SuperSymmetry.SU5.ChargeSpectrum.ZModCharges (n : ℕ) [NeZero n] :
Finset (ChargeSpectrum (ZMod n))

The finite set of ZMod n valued charges which are complete, not pheno-constrained and don't regenerate dangerous couplings with the Yukawa term up-to 4-inserstions of singlets.

Equations
  • One or more equations did not get rendered due to their size.
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    A.2. Finite set of viable ZMod 1 charge spectra is empty #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_one_eq :
    ZModCharges 1 = ∅

    This lemma corresponds to the statement that there are no choices of ℤ₁ representations which give a phenomenologically viable theory.

    A.3. Finite set of viable ZMod 2 charge spectra is empty #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_two_eq :
    ZModCharges 2 = ∅

    This lemma corresponds to the statement that there are no choices of ℤ₂ representations which give a phenomenologically viable theory.

    A.4. Finite set of viable ZMod 3 charge spectra is empty #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_three_eq :
    ZModCharges 3 = ∅

    This lemma corresponds to the statement that there are no choices of ℤ₃ representations which give a phenomenologically viable theory.

    A.5. Finite set of viable ZMod 4 has four elements #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_four_eq :
    ZModCharges 4 = {{ qHd := some 0, qHu := some 2, Q5 := {1}, Q10 := {3} }, { qHd := some 0, qHu := some 2, Q5 := {3}, Q10 := {1} }, { qHd := some 1, qHu := some 2, Q5 := {0}, Q10 := {3} }, { qHd := some 3, qHu := some 2, Q5 := {0}, Q10 := {1} }}

    A.6. Finite set of viable ZMod 5 charge spectra is empty (pseduo result) #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_five_eq :
    ZModCharges 5 = ∅

    This lemma corresponds to the statement that there are no choices of ℤ₅ representations which give a phenomenologically viable theory.

    A.7. Finite set of viable ZMod 6 charge spectra is non-empty (pseduo result) #

    source
    theorem SuperSymmetry.SU5.ChargeSpectrum.ZModCharges_six_eq :
    ZModCharges 6 = {{ qHd := some 0, qHu := some 2, Q5 := {5}, Q10 := {1} }, { qHd := some 0, qHu := some 4, Q5 := {1}, Q10 := {5} }, { qHd := some 1, qHu := some 0, Q5 := {2}, Q10 := {3} }, { qHd := some 1, qHu := some 2, Q5 := {4}, Q10 := {1} }, { qHd := some 1, qHu := some 4, Q5 := {0}, Q10 := {5} }, { qHd := some 1, qHu := some 4, Q5 := {3}, Q10 := {2} }, { qHd := some 2, qHu := some 0, Q5 := {1}, Q10 := {3} }, { qHd := some 2, qHu := some 4, Q5 := {5}, Q10 := {5} }, { qHd := some 3, qHu := some 2, Q5 := {5}, Q10 := {4} }, { qHd := some 3, qHu := some 4, Q5 := {1}, Q10 := {2} }, { qHd := some 4, qHu := some 0, Q5 := {5}, Q10 := {3} }, { qHd := some 4, qHu := some 2, Q5 := {1}, Q10 := {1} }, { qHd := some 5, qHu := some 0, Q5 := {4}, Q10 := {3} }, { qHd := some 5, qHu := some 2, Q5 := {0}, Q10 := {1} }, { qHd := some 5, qHu := some 2, Q5 := {3}, Q10 := {4} }, { qHd := some 5, qHu := some 4, Q5 := {2}, Q10 := {5} }}

    B. The finite set of viable ZMod n × ZMod m charge spectra #

    B.1. General construction #

    source
    def SuperSymmetry.SU5.ChargeSpectrum.ZModZModCharges (n m : ℕ) [NeZero n] [NeZero m] :
    Finset (ChargeSpectrum (ZMod n × ZMod m))

    The finite set of ZMod n × ZMod m valued charges which are complete, not pheno-constrained and don't regenerate dangerous couplings with the Yukawa term up-to 4-inserstions of singlets.

    Equations
    • One or more equations did not get rendered due to their size.
    Instances For