Abstract
We study SU(2) gauge theories coupled to (A1, DN) theories with or without a fundamental hypermultiplet. For even N, a formula for the contribution of (A1, DN) to the Nekrasov partition function was recently obtained by us with Y. Sugawara and T. Uetoko. In this paper, we generalize it to the case of odd N in the classical limit, under the condition that the relevant couplings and vacuum expectation values of Coulomb branch operators of (A1, DN) are all turned off. We apply our formula to the (A2, A5) theory to find that its prepotential is related to that of the SU(2) gauge theory with four fundamental flavors by a simple change of variables.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, Adv. Theor. Math. Phys. 7 (2003) 831 [hep-th/0206161] [INSPIRE].
N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, Prog. Math. 244 (2006) 525 [hep-th/0306238] [INSPIRE].
N.A. Nekrasov and S.L. Shatashvili, Quantization of integrable systems and four dimensional gauge theories, in 16th International Congress on Mathematical Physics, World Scientific (2009), p. 265 [arXiv:0908.4052] [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].
N. Wyllard, AN−1 conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories, JHEP 11 (2009) 002 [arXiv:0907.2189] [INSPIRE].
G. Bonelli, K. Maruyoshi and A. Tanzini, Wild quiver gauge theories, JHEP 02 (2012) 031 [arXiv:1112.1691] [INSPIRE].
D. Gaiotto and J. Teschner, Irregular singularities in Liouville theory and Argyres-Douglas type gauge theories, I, JHEP 12 (2012) 050 [arXiv:1203.1052] [INSPIRE].
T. Kimura, T. Nishinaka, Y. Sugawara and T. Uetoko, Argyres-Douglas theories, S-duality and AGT correspondence, JHEP 04 (2021) 205 [arXiv:2012.14099] [INSPIRE].
S. Giacomelli, N. Mekareeya and M. Sacchi, New aspects of Argyres-Douglas theories and their dimensional reduction, JHEP 03 (2021) 242 [arXiv:2012.12852] [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
V.A. Alba, V.A. Fateev, A.V. Litvinov and G.M. Tarnopolskiy, On combinatorial expansion of the conformal blocks arising from AGT conjecture, Lett. Math. Phys. 98 (2011) 33 [arXiv:1012.1312] [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-twisting and 4d/2d correspondences, arXiv:1006.3435 [INSPIRE].
P.C. Argyres and M.R. Douglas, New phenomena in SU(3) supersymmetric gauge theory, Nucl. Phys. B 448 (1995) 93 [hep-th/9505062] [INSPIRE].
P.C. Argyres, M.R. Plesser, N. Seiberg and E. Witten, New N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 461 (1996) 71 [hep-th/9511154] [INSPIRE].
T. Eguchi, K. Hori, K. Ito and S.-K. Yang, Study of N = 2 superconformal field theories in four-dimensions, Nucl. Phys. B 471 (1996) 430 [hep-th/9603002] [INSPIRE].
R. Flume and R. Poghossian, An algorithm for the microscopic evaluation of the coefficients of the Seiberg-Witten prepotential, Int. J. Mod. Phys. A 18 (2003) 2541 [hep-th/0208176] [INSPIRE].
U. Bruzzo, F. Fucito, J.F. Morales and A. Tanzini, Multiinstanton calculus and equivariant cohomology, JHEP 05 (2003) 054 [hep-th/0211108] [INSPIRE].
F. Fucito, J.F. Morales and R. Poghossian, Instantons on quivers and orientifolds, JHEP 10 (2004) 037 [hep-th/0408090] [INSPIRE].
T.W. Grimm, A. Klemm, M. Marino and M. Weiss, Direct integration of the topological string, JHEP 08 (2007) 058 [hep-th/0702187] [INSPIRE].
M. Del Zotto, C. Vafa and D. Xie, Geometric engineering, mirror symmetry and 6d(1,0) → 4d(N=2), JHEP 11 (2015) 123 [arXiv:1504.08348] [INSPIRE].
S. Cecotti and M. Del Zotto, Higher S-dualities and Shephard-Todd groups, JHEP 09 (2015) 035 [arXiv:1507.01799] [INSPIRE].
M. Buican and T. Nishinaka, Argyres-Douglas theories, the Macdonald index, and an RG inequality, JHEP 02 (2016) 159 [arXiv:1509.05402] [INSPIRE].
M. Buican, S. Giacomelli, T. Nishinaka and C. Papageorgakis, Argyres-Douglas theories and S-duality, JHEP 02 (2015) 185 [arXiv:1411.6026] [INSPIRE].
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].
P.C. Argyres, M.R. Plesser and A.D. Shapere, The Coulomb phase of N = 2 supersymmetric QCD, Phys. Rev. Lett. 75 (1995) 1699 [hep-th/9505100] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
M. Buican and T. Nishinaka, N = 4 SYM, Argyres-Douglas theories, and an exact graded vector space isomorphism, JHEP 04 (2022) 028 [arXiv:2012.13209] [INSPIRE].
S. Cecotti and M. Del Zotto, Infinitely many N = 2 SCFT with ADE flavor symmetry, JHEP 01 (2013) 191 [arXiv:1210.2886] [INSPIRE].
K. Ito, S. Kanno and T. Okubo, Quantum periods and prepotential in N = 2 SU(2) SQCD, JHEP 08 (2017) 065 [arXiv:1705.09120] [INSPIRE].
K. Ito and T. Okubo, Quantum periods for N = 2 SU(2) SQCD around the superconformal point, Nucl. Phys. B 934 (2018) 356 [arXiv:1804.04815] [INSPIRE].
K. Ito, S. Koizumi and T. Okubo, Quantum Seiberg-Witten curve and universality in Argyres-Douglas theories, Phys. Lett. B 792 (2019) 29 [arXiv:1903.00168] [INSPIRE].
K. Ito, S. Koizumi and T. Okubo, Quantum Seiberg-Witten periods for N = 2 SU(Nc) SQCD around the superconformal point, Nucl. Phys. B 954 (2020) 115004 [arXiv:2001.08891] [INSPIRE].
T. Nishinaka and C. Rim, Matrix models for irregular conformal blocks and Argyres-Douglas theories, JHEP 10 (2012) 138 [arXiv:1207.4480] [INSPIRE].
A. Grassi and J. Gu, Argyres-Douglas theories, Painlevé II and quantum mechanics, JHEP 02 (2019) 060 [arXiv:1803.02320] [INSPIRE].
H. Itoyama, T. Oota and K. Yano, Discrete Painlevé system and the double scaling limit of the matrix model for irregular conformal block and gauge theory, Phys. Lett. B 789 (2019) 605 [arXiv:1805.05057] [INSPIRE].
H. Itoyama, T. Oota and K. Yano, Discrete Painlevé system for the partition function of Nf = 2 SU(2) supersymmetric gauge theory and its double scaling limit, J. Phys. A 52 (2019) 415401 [arXiv:1812.00811] [INSPIRE].
H. Itoyama and K. Yano, Theory space of one unitary matrix model and its critical behavior associated with Argyres-Douglas theory, Int. J. Mod. Phys. A 36 (2021) 2150227 [arXiv:2103.11428] [INSPIRE].
T. Oota, Perturbation of multi-critical unitary matrix models, double scaling limits, and Argyres-Douglas theories, Nucl. Phys. B 976 (2022) 115718 [arXiv:2112.14441] [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: 2206.10937
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
Kimura, T., Nishinaka, T. On the Nekrasov partition function of gauged Argyres-Douglas theories. J. High Energ. Phys. 2023, 30 (2023). https://doi.org/10.1007/JHEP01(2023)030
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP01(2023)030