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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!