Gauge-Higgs Unification Models in Six Dimensions with 𝑆²/𝑍₂ Extra Space and GUT Gauge Symmetry

Table 1

Commutation relations of 𝑄^{𝑥(−3−22)}, 𝑄_𝑥(32−2), 𝑄_𝛼, 𝑄_𝑌, 𝑄, and 𝑄_𝐼.

[𝑄^𝑥(−3−22),𝑄𝑦(32−2)]=−3𝛿10^𝑥𝑦𝑄𝑌+−15𝛿^𝑥𝑦𝑄+𝛿^𝑥𝑦𝑄𝐼+1√2(𝜎^∗𝛼)^𝑥𝑦𝑄𝛼
[𝑄𝛼,𝑄𝑥1]=−√2(𝜎𝛼)^𝑦𝑥𝑄𝑦,	[𝑄𝛼,𝑄^𝑥1]=√2(𝜎^∗𝛼)^𝑥𝑦𝑄^𝑦,
[𝑄𝑥,𝑄𝑦]=0,	[𝑄𝑌,𝑄^𝑥]=−3𝑄10^𝑥,
[𝑄,𝑄^𝑥]=−15𝑄^𝑥,	[𝑄𝐼,𝑄^𝑥]=𝑄^𝑥,