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 ).

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


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

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)

Revised on January 29, 2015 09:04:50 by Urs Schreiber (