Abstract
We present the unrefined instanton partition functions of various 5d gauge theories with matter beyond the fundamental representation as sums over Young diagrams. By using these explicit expressions, we verify a range of identities among the instanton partition functions predicted by Higgsing procedures of fivebrane web diagrams and representation theory.
Article PDF
Similar content being viewed by others
References
N. Seiberg and E. Witten, Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD, Nucl. Phys. B 431 (1994) 484 [hep-th/9408099] [INSPIRE].
N. Seiberg and E. Witten, Electric-magnetic duality, monopole condensation, and confinement in N = 2 supersymmetric Yang-Mills theory, Nucl. Phys. B 426 (1994) 19 [hep-th/9407087] [INSPIRE].
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
M. Aganagic, A. Klemm, M. Marino and C. Vafa, The topological vertex, Commun. Math. Phys. 254 (2005) 425 [hep-th/0305132] [INSPIRE].
H. Awata and H. Kanno, Instanton counting, Macdonald functions and the moduli space of D-branes, JHEP 05 (2005) 039 [hep-th/0502061] [INSPIRE].
A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, JHEP 10 (2009) 069 [hep-th/0701156] [INSPIRE].
L.F. Alday, D. Gaiotto and Y. Tachikawa, Liouville correlation functions from four-dimensional gauge theories, Lett. Math. Phys. 91 (2010) 167 [arXiv:0906.3219] [INSPIRE].
S. Nawata and R.-D. Zhu, Instanton counting and O-vertex, JHEP 09 (2021) 190 [arXiv:2107.03656] [INSPIRE].
H. Hayashi and R.-D. Zhu, More on topological vertex formalism for 5-brane webs with O5-plane, JHEP 04 (2021) 292 [arXiv:2012.13303] [INSPIRE].
N. Nekrasov and S. Shadchin, ABCD of instantons, Commun. Math. Phys. 252 (2004) 359 [hep-th/0404225] [INSPIRE].
S. Shadchin, On certain aspects of string theory/gauge theory correspondence, Ph.D. thesis, Université Paris-Sud, Orsay, France (2005) [hep-th/0502180] [INSPIRE].
H.-C. Kim, S.-S. Kim and K. Lee, 5-dim superconformal index with enhanced En global symmetry, JHEP 10 (2012) 142 [arXiv:1206.6781] [INSPIRE].
H.-C. Kim, J. Kim and S. Kim, Instantons on the 5-sphere and M5-branes, arXiv:1211.0144 [KIAS-P12070] [INSPIRE].
C. Hwang, J. Kim, S. Kim and J. Park, General instanton counting and 5d SCFT, JHEP 07 (2015) 063 [Addendum ibid. 04 (2016) 094] [arXiv:1406.6793] [INSPIRE].
O. Bergman and G. Zafrir, Lifting 4d dualities to 5d, JHEP 04 (2015) 141 [arXiv:1410.2806] [INSPIRE].
O. Bergman and G. Zafrir, 5d fixed points from brane webs and O7-planes, JHEP 12 (2015) 163 [arXiv:1507.03860] [INSPIRE].
G. Zafrir, Brane webs and O5-planes, JHEP 03 (2016) 109 [arXiv:1512.08114] [INSPIRE].
H. Hayashi and G. Zoccarato, Partition functions of web diagrams with an O7−-plane, JHEP 03 (2017) 112 [arXiv:1609.07381] [INSPIRE].
S.-S. Kim and F. Yagi, Topological vertex formalism with O5-plane, Phys. Rev. D 97 (2018) 026011 [arXiv:1709.01928] [INSPIRE].
H.-C. Kim et al., 6d strings and exceptional instantons, Phys. Rev. D 103 (2021) 025012 [arXiv:1801.03579] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, 5-brane webs for 5d N = 1 G2 gauge theories, JHEP 03 (2018) 125 [arXiv:1801.03916] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Dualities and 5-brane webs for 5d rank 2 SCFTs, JHEP 12 (2018) 016 [arXiv:1806.10569] [INSPIRE].
S. Cheng and S.-S. Kim, Refined topological vertex for a 5D Sp(N) gauge theories with antisymmetric matter, Phys. Rev. D 104 (2021) 086004 [arXiv:1809.00629] [INSPIRE].
H. Hayashi, S.-S. Kim, K. Lee and F. Yagi, Rank-3 antisymmetric matter on 5-brane webs, JHEP 05 (2019) 133 [arXiv:1902.04754] [INSPIRE].
H.-C. Kim, M. Kim and S.-S. Kim, Topological vertex for 6d SCFTs with Z2-twist, JHEP 03 (2021) 132 [arXiv:2101.01030] [INSPIRE].
S.-S. Kim and X.-Y. Wei, Refined topological vertex with ON-planes, JHEP 08 (2022) 006 [arXiv:2201.12264] [INSPIRE].
A.S. Losev, A. Marshakov and N.A. Nekrasov, Small instantons, little strings and free fermions, in the proceedings of From fields to strings: circumnavigating theoretical physics. A conference in tribute to Ian Kogan, (2003), p. 581 [hep-th/0302191] [INSPIRE].
L.C. Jeffrey and F.C. Kirwan, Localization for non-abelian group actions, alg-geom/9307001.
F. Benini, R. Eager, K. Hori and Y. Tachikawa, Elliptic genera of 2d N = 2 gauge theories, Commun. Math. Phys. 333 (2015) 1241 [arXiv:1308.4896] [INSPIRE].
S.-S. Kim, X. Li, S. Nawata and F. Yagi, Higgsing and tuning D-branes with O-planes, work in progress.
J. Kim et al., Instantons from blow-up, JHEP 11 (2019) 092 [Erratum ibid. 06 (2020) 124] [arXiv:1908.11276] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
A. Hanany and E. Witten, Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics, Nucl. Phys. B 492 (1997) 152 [hep-th/9611230] [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 1, hep-th/9809187 [HUTP-98-A069] [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 2, hep-th/9812127 [HUTP-98-A070] [INSPIRE].
S.H. Katz, A. Klemm and C. Vafa, Geometric engineering of quantum field theories, Nucl. Phys. B 497 (1997) 173 [hep-th/9609239] [INSPIRE].
S. Katz, P. Mayr and C. Vafa, Mirror symmetry and exact solution of 4D N = 2 gauge theories: 1, Adv. Theor. Math. Phys. 1 (1998) 53 [hep-th/9706110] [INSPIRE].
R. Pandharipande and R.P. Thomas, Stable pairs and BPS invariants, Electron. Res. Announ. AMS 23 (2010) 267 [arXiv:0711.3899] [INSPIRE].
D. Maulik and Y. Toda, Gopakumar-Vafa invariants via vanishing cycles, arXiv:1610.07303 [INSPIRE].
A. Iqbal and A.-K. Kashani-Poor, Instanton counting and Chern-Simons theory, Adv. Theor. Math. Phys. 7 (2003) 457 [hep-th/0212279] [INSPIRE].
A. Iqbal and A.-K. Kashani-Poor, SU(N) geometries and topological string amplitudes, Adv. Theor. Math. Phys. 10 (2006) 1 [hep-th/0306032] [INSPIRE].
T. Eguchi and H. Kanno, Topological strings and Nekrasov’s formulas, JHEP 12 (2003) 006 [hep-th/0310235] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2301.02342
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Chen, Y., Jiang, J., Nawata, S. et al. Instantons on Young diagrams with matters. J. High Energ. Phys. 2023, 120 (2023). https://doi.org/10.1007/JHEP03(2023)120
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2023)120