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Towards a 4d/2d correspondence for Sicilian quivers · Around

2011

Towards a 4d/2d correspondence for Sicilian quivers

Hollands, Lotte, Keller, Christoph A., Song, Jaewon

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We study the 4d/2d AGT correspondence between four-dimensional instanton counting and two-dimensional conformal blocks for generalized SU(2) quiver gauge theories coming from punctured Gaiotto curves of arbitrary genus.

We propose a conformal block description that corresponds to the elementary SU(2) trifundamental half-hypermultiplet, and check it against Sp(1)-SO(4) instanton counting.

Built on

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M. R. Gaberdiel, A. Neitzke, “Rationality, quasirationality and finite W-algebras,” Commun. Math. Phys. 238
2003
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U. Bruzzo, F. Fucito, J. F. Morales and A. Tanzini, “Multi-Instanton Calculus and Equivariant Cohomology,” JHEP 0305
2003
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Similar

N. Nekrasov and S. Shadchin, “ABCD of Instantons,” Commun. Math. Phys. 252
2004
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N. A. Nekrasov, “Seiberg-Witten Prepotential from Instanton Counting,” Adv. Theor. Math. Phys. 7
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P. C. Argyres, N. Seiberg, “S-duality in N=2 supersymmetric gauge theories,” JHEP 0712
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2007
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N. Wyllard, “A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories,” JHEP 0911
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F. Benini, S. Benvenuti and Y. Tachikawa, “Webs of five-branes and N=2 superconformal field theories,” JHEP 0909
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2009
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D. Gaiotto, “ 𝒩 = 2 {\mathcal{N}}\!=2 Dualities,” arXiv:0904.2715 [hep-th]
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Cited in the paper.
G. Bonelli, K. Maruyoshi, A. Tanzini, F. Yagi, “Generalized matrix models and AGT correspondence at all genera,” [arXiv:1011.5417 [hep-th]]
Original
Cited in the paper.
Y. Tachikawa, “Six-dimensional D N D_{N} theory and four-dimensional S O − U S p SO-USp quivers,” arXiv:0905.4074 [hep-th]
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Cited in the paper.
O. Chacaltana, J. Distler, “Tinkertoys for the D N D_{N} series,” [arXiv:1106.5410 [hep-th]]
Original
Cited in the paper.
D. Gaiotto, “Asymptotically free N=2 theories and irregular conformal blocks,” [arXiv:0908.0307 [hep-th]]
Original
Cited in the paper.
S. Shadchin, “On Certain Aspects of String Theory / Gauge Theory Correspondence,” arXiv:hep-th/0502180
Cited in the paper.
S. Cecotti, C. Vafa, “Classification of complete N=2 supersymmetric theories in 4 dimensions,” [arXiv:1103.5832 [hep-th]]
Original
Cited in the paper.

Then

L. F. Alday, D. Gaiotto and Y. Tachikawa, “Liouville Correlation Functions from Four-Dimensional Gauge Theories,” Lett. Math. Phys. 91
Original
2010
Later among the works it cites.
O. Chacaltana and J. Distler, “Tinkertoys for Gaiotto Duality,” JHEP 1011
Original
2010
Later among the works it cites.
L. Hollands, C. A. Keller and J. Song, “From SO/Sp Instantons to W-Algebra Blocks,” JHEP 1103
Original
2011
Closest in time.
C. Kozcaz, S. Pasquetti and N. Wyllard, “A & B model approaches to surface operators and Toda theories,” JHEP 1008
Original
2025
Closest in time.
A. Marshakov, A. Mironov, A. Morozov, “On non-conformal limit of the AGT relations,” Phys. Lett. B682
Original

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