Abstract
In this chapter we start with the analysis of \(\mathop{\mathrm{SU}}(2)\) gauge theory with N f = 4 flavors. We will see that it can naturally generalized to the analysis of a whole zoo of theories with the gauge group of the form \(\mathop{\mathrm{SU}}(2)^{n}\). The discussions basically follow the first half of the seminal paper [2].
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Notes
- 1.
The author thanks Jacques Distler for very illuminating discussions on this point.
- 2.
Hitchin himself called \(\varphi (z)\) the Higgs field, but the author thinks this terminology is rather confusing in the \(\mathcal{N}=2\) supersymmetric context, as \(\varphi (z)\) controls the physics of the Coulomb branch, not of the Higgs branch.
References
P.C. Argyres, A. Buchel, New S-dualities in \(\mathcal{N}\! = 2\) supersymmetric SU(2) × SU(2) Gauge theory. J. High Energy Phys. 11, 014 (1999). arXiv:hep-th/9910125
D. Gaiotto, \(\mathcal{N}\! = 2\) dualities. J. High Energy Phys. 1208, 034 (2012). arXiv:0904.2715 [hep-th]
D. Gaiotto, G.W. Moore, A. Neitzke, Wall-crossing, Hitchin systems, and the WKB approximation. Adv. Math. 234, 239–403 (2013). arXiv:0907.3987 [hep-th]
N. Seiberg, E. Witten, Monopoles, duality and chiral symmetry breaking in \(\mathcal{N}\! = 2\) supersymmetric QCD. Nucl. Phys. B431, 484–550 (1994). arXiv:hep-th/9408099
J. Song, 4d/2d correspondence: instantons and W-algebras. Ph.D. thesis (2012). http://thesis.library.caltech.edu/7103/
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Tachikawa, Y. (2015). \(\mathop{\mathrm{SU}}(2)\) Theory with Four Flavors and Gaiotto’s Duality. In: N=2 Supersymmetric Dynamics for Pedestrians. Lecture Notes in Physics, vol 890. Springer, Cham. https://doi.org/10.1007/978-3-319-08822-8_9
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DOI: https://doi.org/10.1007/978-3-319-08822-8_9
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