{
 "id": "su3_hy",
 "group": "SU(3) 5D",
 "orbifold": {
  "name": "S1/Z2"
 },
 "source": {
  "paper": "N. Haba, T. Yamashita, JHEP 02 (2004) 059 (hep-ph/0401185), eq. (3.20)",
  "extracted_from": "research/smeft_formalization/part_vii/hy_predictions.py",
  "chain": "hy_predictions.py defines their eq. (3.20) as hy_table(); this file evaluates it on unit contents to extract the coefficient table, and copies the archived prediction bank verbatim",
  "date": "2026-08-26"
 },
 "reps": {
  "adjoint": {
   "(+,+)": 1,
   "(+,-)": 1
  },
  "fund": {
   "(+,+)": 1,
   "(+,-)": 1
  },
  "scalar": {
   "(+,+)": 1,
   "(+,-)": 1
  }
 },
 "species": {
  "adjoint": "adjoint Dirac fermion (4 dof)",
  "fund": "fundamental Dirac fermion (2 dof per pair)",
  "scalar": "complex scalar (-2 dof)"
 },
 "terms5d": [
  {
   "c": 2,
   "s": 1,
   "base": -1.5,
   "per": {
    "Nap": 2.0
   }
  },
  {
   "c": 2,
   "s": -1,
   "base": 0.0,
   "per": {
    "Nam": 2.0
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  },
  {
   "c": 1,
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   "base": -3.0,
   "per": {
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    "Nsp": -1.0
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  {
   "c": 1,
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   "per": {
    "Nam": 4.0,
    "Nfm": 2.0,
    "Nsm": -1.0
   }
  }
 ],
 "census": {
  "vacua": 1277,
  "max_each": 4,
  "source": "hy_predictions.py: every content up to four of each species"
 },
 "vgiq": {
  "charges": {
   "SU(2)": {
    "adj": [
     -2,
     0,
     2
    ],
    "fund": [
     -1,
     1
    ],
    "CG": 2.0,
    "CR": 0.5
   },
   "SU(3)": {
    "adj": [
     -2,
     -1,
     -1,
     0,
     0,
     1,
     1,
     2
    ],
    "fund": [
     -1,
     0,
     1
    ],
    "CG": 3.0,
    "CR": 0.5
   }
  },
  "critical_nf": [
   {
    "group": "SU(2)",
    "rep": "fund",
    "nf_ours": 3.0,
    "nf_theirs": 3.0
   },
   {
    "group": "SU(3)",
    "rep": "fund",
    "nf_ours": 4.5,
    "nf_theirs": 4.5
   },
   {
    "group": "SU(2)",
    "rep": "adj",
    "nf_ours": 0.75,
    "nf_theirs": 0.75
   },
   {
    "group": "SU(3)",
    "rep": "adj",
    "nf_ours": 0.75,
    "nf_theirs": 0.75
   }
  ],
  "minima_ours": {
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   "SU(3)": 0.3333333333333333
  },
  "minima_theirs": {
   "SU(2)": 0.25,
   "SU(3)": 0.29
  },
  "polyakov_at_theirs_su3": 0.16754008,
  "source": "vgiq_anchor.py against von Gersdorff-Irges-Quiros hep-th/0204223: charges from explicit generators, their alpha = 2 omega convention from their own footnotes; four critical flavour numbers exact, the SU(2) minimum exact, and the SU(3) minimum UNRESOLVED -- ours is exactly 1/3, on the Z3 centre, where the fundamental Polyakov loop vanishes; theirs prints 0.29 = (1/3)(sqrt3/2) to two digits, a normalisation their text fixes for SU(2) and not for SU(3). Reported with the evidence, not claimed as a slip"
 },
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  },
  {
   "alpha": 0.04366609044393553,
   "D": 0.5,
   "A4": 89.0,
   "Fpp": 9.108792710034612,
   "content": {
    "Nap": 3,
    "Nam": 4,
    "Nfp": 4,
    "Nfm": 1,
    "Nsp": 0,
    "Nsm": 4
   }
  },
  {
   "alpha": 0.04377389060266142,
   "D": 0.5,
   "A4": 83.0,
   "Fpp": 9.2818237755668,
   "content": {
    "Nap": 3,
    "Nam": 3,
    "Nfp": 1,
    "Nfm": 1,
    "Nsp": 0,
    "Nsm": 0
   }
  },
  {
   "alpha": 0.04377389060266142,
   "D": 0.5,
   "A4": 83.0,
   "Fpp": 9.2818237755668,
   "content": {
    "Nap": 3,
    "Nam": 3,
    "Nfp": 1,
    "Nfm": 2,
    "Nsp": 0,
    "Nsm": 2
   }
  },
  {
   "alpha": 0.04377389060266142,
   "D": 0.5,
   "A4": 83.0,
   "Fpp": 9.2818237755668,
   "content": {
    "Nap": 3,
    "Nam": 3,
    "Nfp": 1,
    "Nfm": 3,
    "Nsp": 0,
    "Nsm": 4
   }
  },
  {
   "alpha": 0.04377389060266142,
   "D": 0.5,
   "A4": 83.0,
   "Fpp": 9.2818237755668,
   "content": {
    "Nap": 3,
    "Nam": 3,
    "Nfp": 2,
    "Nfm": 1,
    "Nsp": 2,
    "Nsm": 0
   }
  },
  {
   "alpha": 0.04377389060266142,
   "D": 0.5,
   "A4": 83.0,
   "Fpp": 9.2818237755668,
   "content": {
    "Nap": 3,
    "Nam": 3,
    "Nfp": 2,
    "Nfm": 2,
    "Nsp": 2,
    "Nsm": 2
   }
  }
 ],
 "anchor": {
  "label": "the smallest content of the archived bank",
  "bulk": [
   {
    "rep": "adjoint",
    "parities": [
     1,
     1
    ],
    "multiplicity": 2
   },
   {
    "rep": "adjoint",
    "parities": [
     1,
     -1
    ],
    "multiplicity": 2
   },
   {
    "rep": "fund",
    "parities": [
     1,
     1
    ],
    "multiplicity": 2
   },
   {
    "rep": "fund",
    "parities": [
     1,
     -1
    ],
    "multiplicity": 1
   },
   {
    "rep": "scalar",
    "parities": [
     1,
     -1
    ],
    "multiplicity": 1
   }
  ],
  "expected": {
   "alpha": 0.04023454228525068,
   "D": 0.25,
   "A4": 49.0,
   "Fpp": 4.644130753909976
  },
  "caveat": "no absolute scale exists here at all: Haba-Yamashita publish no normalisation, so alpha and the spectrum are in units of 1/R and nothing is a GeV"
 },
 "note": "the 5D class of Part VII section 11: no odd 8D occurs here -- a Dirac fermion enters with 4 dof and a complex scalar with -2, both even, and the odd -3 of gauge+ghost multiplies only the adjoint, evenly. The odd rung the ceiling stands on needs the sixth dimension."
}