The BF model is a topological field theory, which when quantized, becomes a topological quantum field theory. BF stands for background field. B and F, as can be seen below, are also the variables appearing in the Lagrangian of the theory, which is helpful as a mnemonic device.
The action is given by
- (no curvature)
- (the covariant exterior derivative of B is zero).
In fact, it is always possible to gauge away any local degrees of freedom, which is why it is called a topological field theory.
However, if M is topologically nontrivial, A and B can have nontrivial solutions globally.
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