Built on

Van Nostrand, 1993
D. H. Collingwood and W. M. McGovern, Nilpotent orbits in semisimple Lie algebras · 1993
Earlier work this paper cites.
P. C. Argyres and M. R. Douglas, “New Phenomena in S U ( 3 ) SU(3) Supersymmetric Gauge Theory,” Nucl. Phys
1995
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P. C. Argyres, M. R. Plesser, N. Seiberg, and E. Witten, “New 𝒩 = 2 {\mathcal{N}}\!=2 Superconformal Field Theories in Four Dimensions,” Nucl. Phys
1996
Earlier work this paper cites.
J. A. Minahan and D. Nemeschansky, “An 𝒩 = 2 {\mathcal{N}}\!=2 Superconformal Fixed Point with E 6 E_{6} Global Symmetry,” Nucl. Phys
1996
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J. A. Minahan and D. Nemeschansky, “Superconformal Fixed Points with E N E_{N} Global Symmetry,” Nucl. Phys
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S. Katz, P. Mayr, and C. Vafa, “Mirror Symmetry and Exact Solution of 4D 𝒩 = 2 {\mathcal{N}}\!=2 Gauge Theories. I,” Adv. Theor. Math. Phys
1998
Earlier work this paper cites.

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Then

F. Benini, S. Benvenuti, and Y. Tachikawa, “Webs of Five-Branes and 𝒩 = 2 {\mathcal{N}}\!=2 Superconformal Field Theories,” JHEP
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2009
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2010
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Y. Tachikawa, “On S-Duality of 5D Super Yang-Mills on S 1 ,” JHEP
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2011
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2012
Closest in time.
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2012

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2012

Gaiotto Duality for the Twisted A_{2N-1} Series

Chacaltana, Oscar, Distler, Jacques, Tachikawa, Yuji

Understand

We study 4D N=2 superconformal theories that arise from the compactification of 6D N=(2,0) theories of type A_{2N-1} on a Riemann surface C, in the presence of punctures twisted by a Z_2 outer automorphism.

We describe how to do a complete classification of these SCFTs in terms of three-punctured spheres and cylinders, which we do explicitly for A_3, and provide tables of properties of twisted defects up through A_9.
We find atypical degenerations of Riemann surfaces that do not lead to weakly-coupled gauge groups, but to a gauge coupling pinned at a point in the interior of moduli space.
As applications, we study: i) 6D representations of 4D superconformal quivers in the shape of an affine/non-affine D_n Dynkin diagram, ii) S-duality of SU(4) and Sp(2) gauge theories with various combinations of fundamental and antisymmetric matter, and iii) realizations of all rank-one SCFTs predicted by Argyres and Wittig.

Built on

Van Nostrand, 1993
D. H. Collingwood and W. M. McGovern, Nilpotent orbits in semisimple Lie algebras · 1993
Earlier work this paper cites.
P. C. Argyres and M. R. Douglas, “New Phenomena in S U ( 3 ) SU(3) Supersymmetric Gauge Theory,” Nucl. Phys
1995
Earlier work this paper cites.
P. C. Argyres, M. R. Plesser, N. Seiberg, and E. Witten, “New 𝒩 = 2 {\mathcal{N}}\!=2 Superconformal Field Theories in Four Dimensions,” Nucl. Phys
1996
Earlier work this paper cites.
J. A. Minahan and D. Nemeschansky, “An 𝒩 = 2 {\mathcal{N}}\!=2 Superconformal Fixed Point with E 6 E_{6} Global Symmetry,” Nucl. Phys
1996
Earlier work this paper cites.
J. A. Minahan and D. Nemeschansky, “Superconformal Fixed Points with E N E_{N} Global Symmetry,” Nucl. Phys
1997
Earlier work this paper cites.
S. Katz, P. Mayr, and C. Vafa, “Mirror Symmetry and Exact Solution of 4D 𝒩 = 2 {\mathcal{N}}\!=2 Gauge Theories. I,” Adv. Theor. Math. Phys
1998
Earlier work this paper cites.

Similar

A. Kapustin, “ D N D_{N} Quivers from Branes,” JHEP
1998
Cited alongside, same era.
E. Sommers, “Lusztig’s canonical quotient and generalized duality,” J. Algebra
2001
Cited alongside, same era.
P. N. Achar and E. N. Sommers, “Local systems on nilpotent orbits and weighted Dynkin diagrams,” Represent. Theory
2002
Cited alongside, same era.
P. N. Achar, “An order-reversing duality map for conjugacy classes in Lusztig’s canonical quotient,” Transform. Groups
2003
Cited alongside, same era.
Y. Tachikawa, “Six-Dimensional D N D_{N} Theory and Four-Dimensional SO-USp Quivers,” JHEP
Original
2009
Cited alongside, same era.
D. Nanopoulos and D. Xie, “ 𝒩 = 2 {\mathcal{N}}\!=2 Su Quiver with Usp Ends Or Su Ends with Antisymmetric Matter,” JHEP