# nLab geometric engineering of quantum field theory

Contents

### Context

#### Quantum field theory

functorial quantum field theory

# Contents

## Idea

By embedding quantum field theories into string theory – typically as the worldvolume theories of various branes, e.g. super Yang-Mills theory on D-branes, 6d (2,0)-superconformal QFT on M5-branes, or else at O-planes – the various dualities of string theory will relate different QFTs in way that are typically far from obvious from just looking at these QFTs themselves.

The investigation specifically of N=2 D=4 super Yang-Mills theory and N=1 D=4 super Yang-Mills theory in this fashion has come to be known as geometric engineering of quantum field theory (Katz-Klemm-Vafa 97, Katz-Klemm 96 ).

Specifically, the geometrically engineered QFTs are those on the worldvolume of black D-branes that end on (are suspended between) black NS5-branes (due to Hanany-Witten 97, review includes Fazzi 17). See at D-branes ending on NS5-branes.

graphics grabbed from Fazzi 17, p. 25

graphics grabbed from Fazzi 17, p. 32

For more relations between QFTs found via string theory see at string theory results applied elsewhere.

## References

### General

The original articles are

Review:

Further developments are in

• Balázs Szendrői, Nekrasov’s Partition Function and Refined Donaldson–Thomas Theory: the Rank One Case, SIGMA, 2012, Volume 8, 088 (web)

### Examples

#### Geometric engineering of $D = 6$$\mathcal{N} = (1,0)$ SCFT

On D=6 N=(1,0) SCFTs via geometric engineering on M5-branes/NS5-branes at D-, E-type ADE-singularities, notably from M-theory on S1/G_HW times H/G_ADE, hence from orbifolds of type I' string theory (see at half NS5-brane):

Last revised on August 11, 2020 at 16:34:19. See the history of this page for a list of all contributions to it.