nLab geometric engineering of quantum field theory



Quantum field theory


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

String theory



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.



The original articles are


Further developments are in

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


Geometric engineering of D=6D = 6 𝒩=(2,0)\mathcal{N} = (2,0) SCFT

For geometric engineering of the D=6 N=(2,0) SCFT, see at duality between M-theory on Z2-orbifolds and type IIB string theory on K3-fibrations – Geometric engineering of 6d (2,0)-SCFT.

Geometric engineering of D=6D = 6 𝒩=(1,0)\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 October 13, 2022 at 16:00:52. See the history of this page for a list of all contributions to it.