functorial quantum field theory
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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
Sheldon Katz, Albrecht Klemm, Cumrun Vafa, Geometric Engineering of Quantum Field Theories, Nucl.Phys. B497 (1997) 173-195 (arXiv:hep-th/9609239)
Sheldon Katz, Cumrun Vafa, Geometric Engineering of $N=1$ Quantum Field Theories, Nucl.Phys. B497 (1997) 196-204 (arXiv:hep-th/9611090)
Amihay Hanany, Edward Witten, Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics, Nucl. Phys. B492:152-190, 1997 (arXiv:hep-th/9611230)
Review:
Amit Giveon, David Kutasov, Brane Dynamics and Gauge Theory, Rev. Mod. Phys. 71:983-1084, 1999 (arXiv:hep-th/9802067)
(emphasis on the s-rule)
Andreas Karch, Field Theory Dynamics from Branes in String Theory, PhD thesis (1998) (doi:10.18452/14371)
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
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.
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):
Michele Del Zotto, Jonathan Heckman, Alessandro Tomasiello, Cumrun Vafa, 6d Conformal Matter, JHEP02(2015)054 (arXiv:1407.6359)
Davide Gaiotto, Alessandro Tomasiello, Holography for $(1,0)$ theories in six dimensions, JHEP12(2014)003 (arXiv:1404.0711)
Kantaro Ohmori, Hiroyuki Shimizu, $S^1/T^2$ Compactifications of 6d $\mathcal{N} = (1,0)$ Theories and Brane Webs, J. High Energ. Phys. (2016) 2016: 24 (arXiv:1509.03195)
Hirotaka Hayashi, Sung-Soo Kim, Kimyeong Lee, Futoshi Yagi, 6d SCFTs, 5d Dualities and Tao Web Diagrams, JHEP05 (2019)203 (arXiv:1509.03300)
Ibrahima Bah, Achilleas Passias, Alessandro Tomasiello, $AdS_5$ compactifications with punctures in massive IIA supergravity, JHEP11 (2017)050 (arXiv:1704.07389)
Last revised on August 11, 2020 at 16:34:19. See the history of this page for a list of all contributions to it.