nLab
geometric engineering of quantum field theory

Contents

Context

Quantum field theory

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

String 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.

Examples

References

The original articles are

Reviews include

  • Andreas Karch, Field Theory Dynamics from Branes in String Theory, PhD thesis (1998) pdf

  • David Morrison, Limitations of Geometric Engineering:

    Implications for Model Building_, talk (2008) pdf slides

  • Marco Fazzi, Higher-dimensional field theories from type II supergravity (arXiv:1712.04447)

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)

Last revised on November 28, 2018 at 02:15:26. See the history of this page for a list of all contributions to it.