cohomological field theory



The term “cohomological field theory” is mostly used for the “Witten style” topological quantum field theories which arise from a topological twist of a supersymmetric quantum field theory, notable example being the A-model and the B-model topological string.

Mathematically these topological field theories came to be known as TCFTs. With the proof of the cobordism hypothesis these were understood to be the “non-compact” 2-dimensional extended TQFTs with codomain an (infinity,1)-category of chain complexes, where “non-compact” refers to all cobordisms being required to have non-empty outgoing boundary.

For more on all this see at TCFT and at 2d TQFT.


  • Edward Witten, Introduction to cohomological field theory, InternationalJournal of Modern Physics A, Vol. 6,No 6 (1991) 2775-2792 (pdf)

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