nLab
Kapustin-Witten TQFT

Idea

A 4d TQFT obtained by a “topological twist” from 4d super Yang-Mills theory. Its S-duality is supposed to encode, as a special case geometric Langlands duality.

Upon compactification down to 2d it reproduces, at certain parameters, the A-model and the B-model.

Related concepts

• geometric Langlands duality

• A-model, B-model

References

The TQFT was introduced in

• Anton Kapustin, Edward Witten, Electric-Magnetic Duality And The Geometric Langlands Program , Communications in number theory and physics, Volume 1, Number 1, 1–236 (2007) (arXiv:hep-th/0604151)

Reviews include

• Anton Kapustin, Langlands Duality and Topological Field Theory (2007) (pdf)

The 0-1-2 extended QFT version of $\mathrm{GL}$-twisted N=4 D=4 super Yang-Mills theory is considered in

• David Ben-Zvi, David Nadler, The Character Theory of a Complex Group (arXiv:0904.1247)

A discussion formalized in terms of derived geometry is in

• Kevin Costello, Notes on supersymmetric and holomorphic field theories in dimension 2 and 4 (pdf)