Symmetry Breaking and the Metric

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SUMMARY

The discussion centers on the implications of introducing a B field in 1,2 dimensions within the context of Lie 3 algebras, specifically referencing the paper at http://arxiv.org/abs/0901.1847. It is established that this introduction leads to a symmetry breaking from SO(4) to SO(2) x SO(2) and results in a diagonal metric. The diagonalization of the metric is justified by the residual symmetry group, allowing for a simplified expression akin to obtaining the Minkowski metric in General Relativity.

PREREQUISITES
  • Understanding of Lie 3 algebras
  • Familiarity with symmetry groups, specifically SO(4) and SO(2)
  • Knowledge of B fields in theoretical physics
  • Basic principles of General Relativity and metric tensor
NEXT STEPS
  • Research the properties and applications of Lie 3 algebras
  • Study the implications of B fields in string theory and their effects on symmetry
  • Explore the concept of symmetry breaking in theoretical physics
  • Learn about the process of metric diagonalization in General Relativity
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PhD students in theoretical physics, researchers studying string theory, and anyone interested in the mathematical foundations of symmetry in physics.

Digs
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Hello,


im a first year phd student, and I am 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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