I would like to ask about the case of:(adsbygoogle = window.adsbygoogle || []).push({});

##SU(2)\otimes U(1) \rightarrow U(1)\otimes U(1),## spontaneous symmetry breaking.

It is given that the Wilson Loop:

##W \equiv exp[ig \oint dy H T^1]= diag(−1,−1,1).##

Where ##y## is the ##S^1/Z^2## fifth/extra dimension, ##H = \frac{1}{g R}## and ##T^1## is the first ##SU(3)## generator.

As we can check, the Wilson Loop does not commute with ##SU(3)## generators ##T^6, T^7## but it still commutes with ##T^3, T^8##.

The non-trivial parity in this case is ##P = diag(1,−1,−1)## and it anti-commutes only with ##T^1##.

How does this SSB occur?

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# Wilson Loop and spontaneous symmetry breaking.

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