nLab
Kapustin-Witten TQFT

Context

Quantum field theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Contents

Idea

The Kapustin-Witten TQFT is the 4d TQFT obtained by topological twisting from N=4 D=4 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.

gauge theory induced via AdS-CFT correspondence

M-theory perspective via AdS7-CFT6F-theory perspective
11d supergravity/M-theory
\;\;\;\;\downarrow Kaluza-Klein compactification on S 4S^4compactificationon elliptic fibration followed by T-duality
7-dimensional supergravity
\;\;\;\;\downarrow topological sector
7-dimensional Chern-Simons theory
\;\;\;\;\downarrow AdS7-CFT6 holographic duality
6d (2,0)-superconformal QFT on the M5-brane with conformal invarianceM5-brane worldvolume theory
\;\;\;\; \downarrow KK-compactification on Riemann surfacedouble dimensional reduction on M-theory/F-theory elliptic fibration
N=2 D=4 super Yang-Mills theory with Montonen-Olive S-duality invariance; AGT correspondenceD3-brane worldvolume theory with type IIB S-duality
\;\;\;\;\; \downarrow topological twist
topologically twisted N=2 D=4 super Yang-Mills theory
\;\;\;\; \downarrow KK-compactification on Riemann surface
A-model on Bun GBun_G, Donaldson theory

\,

gauge theory induced via AdS5-CFT4
type II string theory
\;\;\;\;\downarrow Kaluza-Klein compactification on S 5S^5
\;\;\;\; \downarrow topological sector
5-dimensional Chern-Simons theory
\;\;\;\;\downarrow AdS5-CFT4 holographic duality
N=4 D=4 super Yang-Mills theory
\;\;\;\;\; \downarrow topological twist
topologically twisted N=4 D=4 super Yang-Mills theory
\;\;\;\; \downarrow KK-compactification on Riemann surface
A-model on Bun GBun_G and B-model on Log GLog_G, geometric Langlands correspondence

References

The TQFT was introduced in

Reviews include

The 0-1-2 extended QFT version of GLGL-twisted N=4 D=4 super Yang-Mills theory is considered in

A discussion formalized in BV quantization of factorization algebras is in

  • Kevin Costello, Notes on supersymmetric and holomorphic field theories in dimension 2 and 4 (pdf)
Revised on September 30, 2013 12:40:04 by Urs Schreiber (82.113.99.90)