#
nLab

cohomological field theory

Contents
### Context

#### Quantum field theory

# 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

Last revised on December 5, 2019 at 18:58:26.
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