Coupling a QFT to a TQFT and Duality

Understand

We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory.

• On R^d the new theory differs from the original one by the spectrum of operators.
• Sometimes the local operators are the same but there are different line operators, surface operators, etc.
• The effects of the added topological degrees of freedom are more dramatic when we compactify R^d, and they are crucial in the context of electric-magnetic duality.