Coupling a QFT to a TQFT and duality

We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On $ \mathbb{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 $ \mathbb{R} $ d , and they are crucial in the context of electric-magnetic duality. We explore several examples including DijkgraafWitten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological…

• NS
  National Science Foundation

  Awards: 1066293, PHYS-1066293
• UD
  U.S. Department of Energy

  Awards: FG02-92ER40701, DE-FG02-92ER40701, DE-SC0009988, SC0009988, DE-FG02-, DE-FG02
• US
  United States-Israel Binational Science Foundation

  Award: 2010/629