Symmetry Breaking and the Metric

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Hello,


im a first year phd student, and im reading http://arxiv.org/abs/0901.1847 right now in an attempt to figure out something cool to do with lie 3 algebras.

In the paper they mention that turning on a B field in the 1,2 dimensions breaks the SO(4) symmetry the theory has to SO(2)xSO(2), and as well the metric becomes diagonal, with some funny entries I don't recognize.

Why does the metric become diagonal? Also, why does the symmetry break to that?

THanks!
 
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I ain't no expert, but I think what they mean is that a diagonal form like that is allowed (as opposed to: the most general expression you can have). So with the residual symmetry group it's always possible to obtain such an expression for the metric.

Think of it as normal GR. In that case it's always possible to (locally) obtain the Minkowski metric.

That would be my best guess.
 

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