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The quiver approach to the BPS spectrum of a 4d N=2 gauge theory · Around

2012

The quiver approach to the BPS spectrum of a 4d N=2 gauge theory

Cecotti, Sergio

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We present a survey of the computation of the BPS spectrum of a general four-dimensional N=2 supersymmetric gauge theory in terms of the Representation Theory of quivers with superpotential.

We focus on SYM with a general gauge group G coupled to standard matter in arbitrary representations of G (consistent with a non--positive beta--function).
The situation is particularly tricky and interesting when the matter consists of an odd number of half-hypermultiplets: we describe in detail SU(6) SYM coupled to half a 20, SO(12) SYM coupled to half a 32, and E_7 SYM coupled to half a 56.

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W. Crawley–Boevey, “On the exceptional fibres of Kleinian singularities,” Amer. J. Math. 122
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H. Derksen, J. Wyman, and A. Zelevinsky, “Quivers with potentials and their representations I: Mutations,” Selecta Mathematica 14
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Similar

S. Cecotti and M. Del Zotto, On Arnold’s 14 ‘exceptional’ 𝒩 = 2 \mathcal{N}=2 superconformal gauge theories,
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Then

M. Alim, S. Cecotti, C. Cordova, S. Espahbodi, A. Rastogi, and C. Vafa, “BPS Quivers and Spectra of Complete N=2 Quantum Field Theories,” Comm. Math. Phys. 323
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S. Cecotti, “Categorical tinkertoys for N = 2 N=2 gauge theories”, Int. J. Mod. Phys. A 28
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2013
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S. Cecotti and M. Del Zotto, “Infinitely many N=2 SCFT with ADE flavor symmetry,” JHEP 01
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M. Alim, S. Cecotti, C. Cordova, S. Espahbodi, A. Rastogi, and C. Vafa, “ N = 2 N=2 Quantum Field Theories and their BPS Quivers,” Advances in Theor. Math. Phys. 18
Original
2014
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D. Gaiotto, G. W. Moore, and A. Neitzke, “Framed BPS States,” arXiv:1006.0146 [hep-th]

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S. Cecotti, A. Neitzke, and C. Vafa, “R-Twisting and 4d/2d Correspondences,” arXiv:1006.3435 [hep-th]

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D. Gaiotto, “N=2 dualities,” arXiv:0904.2715 [hep-th]

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Y. Tachikawa, “N=2 S S –duality via outer–automorphism twists”, arXiv:1009.0339 [hep-th]

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