nLab cohomological field theory

Redirected from "cohomological quantum field theories".
Contents

Contents

Idea

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.

References

  • Edward Witten, Introduction to cohomological field theory, InternationalJournal of Modern Physics A, Vol. 6,No 6 (1991) 2775-2792 (pdf)
  • M. Kontsevich, Yu. Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164.3 (1994) 525–562
  • Rahul Pandharipande, Cohomological field theory calculations, Proc. ICM 2018 Rio de Janeiro, Vol. 1 (869–898) pdf

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