Abstract
This is the second in a series of three papers on systematic analysis of rank 1 Coulomb branch geometries of four dimensional \( \mathcal{N} \) = 2 SCFTs. In [1] we developed a strategy for classifying physical rank-1 CB geometries of \( \mathcal{N} \) = 2 SCFTs. Here we show how to carry out this strategy computationally to construct the Seiberg-Witten curves and one-forms for all the rank-1 SCFTs. Explicit expressions are given for all 28 cases, with the exception of the N f =4 su(2) gauge theory and the E n SCFTs which were constructed in [2, 3] and [4, 5].
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs. Part I: physical constraints on relevant deformations, JHEP 02 (2018) 001 [arXiv:1505.04814] [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 [Erratum ibid. B 430 (1994) 485] [hep-th/9407087] [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].
J.A. Minahan and D. Nemeschansky, An N = 2 superconformal fixed point with E 6 global symmetry, Nucl. Phys. B 482 (1996) 142 [hep-th/9608047] [INSPIRE].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with E n global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].
L. Bhardwaj and Y. Tachikawa, Classification of 4d N = 2 gauge theories, JHEP 12 (2013) 100 [arXiv:1309.5160] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, L. Rastelli and B.C. van Rees, The \( \mathcal{N} \) = 2 superconformal bootstrap, JHEP 03 (2016) 183 [arXiv:1412.7541] [INSPIRE].
P. Liendo, I. Ramirez and J. Seo, Stress-tensor OPE in \( \mathcal{N} \) = 2 superconformal theories, JHEP 02 (2016) 019 [arXiv:1509.00033] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for Gaiotto duality, JHEP 11 (2010) 099 [arXiv:1008.5203] [INSPIRE].
O. Chacaltana and J. Distler, Tinkertoys for the D N series, JHEP 02 (2013) 110 [arXiv:1106.5410] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the E 6 theory, JHEP 09 (2015) 007 [arXiv:1403.4604] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, A family of 4D \( \mathcal{N} \) = 2 interacting SCFTs from the twisted A 2N series, arXiv:1412.8129 [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Z 3 -twisted D4 theory, arXiv:1601.02077 [INSPIRE].
D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory- Part I: classification, arXiv:1510.01324 [INSPIRE].
D. Xie and S.-T. Yau, Semicontinuity of 4d N = 2 spectrum under renormalization group flow, JHEP 03 (2016) 094 [arXiv:1510.06036] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of N = 2 SCFTs III: enhanced Coulomb branches and central charges, JHEP 02 (2018) 003 [arXiv:1609.04404] [INSPIRE].
P.C. Argyres, M. Lotito, Y. Lü and M. Martone, Expanding the landscape of \( \mathcal{N} \) = 2 rank 1 SCFTs, JHEP 05 (2016) 088 [arXiv:1602.02764] [INSPIRE].
O. DeWolfe and B. Zwiebach, String junctions for arbitrary Lie algebra representations, Nucl. Phys. B 541 (1999) 509 [hep-th/9804210] [INSPIRE].
O. DeWolfe, T. Hauer, A. Iqbal and B. Zwiebach, Uncovering the symmetries on [p, q] seven-branes: beyond the Kodaira classification, Adv. Theor. Math. Phys. 3 (1999) 1785 [hep-th/9812028] [INSPIRE].
K. Kodaira, On the structure of compact complex analytic surfaces. I, Amer. J. Math. 86 (1964) 751.
K. Kodaira, On the structure of compact complex analytic surfaces. II, III, Amer. J. Math. 88 (1966) 682.
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].
P.A.M. Dirac, Quantized singularities in the electromagnetic field, Proc. Roy. Soc. Lond. A 133 (1931) 60 [INSPIRE].
J.S. Schwinger, A magnetic model of matter, Science 165 (1969) 757 [INSPIRE].
D. Zwanziger, Quantum field theory of particles with both electric and magnetic charges, Phys. Rev. 176 (1968) 1489 [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
P.C. Argyres and J. Wittig, Mass deformations of four-dimensional, rank 1, N = 2 superconformal field theories, J. Phys. Conf. Ser. 462 (2013) 012001 [arXiv:1007.5026] [INSPIRE].
G. Shephard and J. Todd, Finite unitary reflection groups, Canadian J. Math. 6 (1954) 274.
C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. of Math. 77 (1955) 778.
S.R. Coleman and J. Mandula, All possible symmetries of the S matrix, Phys. Rev. 159 (1967) 1251 [INSPIRE].
J. Humphreys, Reflection groups and Coxeter groups, Cambridge University Press, Cambridge U.K. (1990).
A. Cohen, Finite complex reflection groups, Ann. Scient. E.N.S. 9 (1976) 379.
P.C. Argyres and M. Ünsal, The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion and renormalon effects, JHEP 08 (2012) 063 [arXiv:1206.1890] [INSPIRE].
K. Dasgupta and S. Mukhi, F theory at constant coupling, Phys. Lett. B 385 (1996) 125 [hep-th/9606044] [INSPIRE].
A. Sen, F theory and orientifolds, Nucl. Phys. B 475 (1996) 562 [hep-th/9605150] [INSPIRE].
T. Banks, M.R. Douglas and N. Seiberg, Probing F-theory with branes, Phys. Lett. B 387 (1996) 278 [hep-th/9605199] [INSPIRE].
E. Brieskorn, Singular elements of semi-simple algebraic groups, Actes Congres intern. Math. 2 (1970) 279.
P. Argyres, M. Lotito, Y. Lü, and M. Martone, to appear.
D. Cox, J. Little and D. O’Shea, Ideals, varieties, and algorithms, 2nd edition, Springer, Germany (1997).
T. Hauer, A. Iqbal and B. Zwiebach, Duality and Weyl symmetry of 7-brane configurations, JHEP 09 (2000) 042 [hep-th/0002127] [INSPIRE].
P.C. Argyres and M. Martone, 4d \( \mathcal{N} \) = 2 theories with disconnected gauge groups, JHEP 03 (2017) 145 [arXiv:1611.08602] [INSPIRE].
M. Noguchi, S. Terashima and S.-K. Yang, N = 2 superconformal field theory with ADE global symmetry on a D3-brane probe, Nucl. Phys. B 556 (1999) 115 [hep-th/9903215] [INSPIRE].
P.C. Argyres and J.R. Wittig, Infinite coupling duals of N = 2 gauge theories and new rank 1 superconformal field theories, JHEP 01 (2008) 074 [arXiv:0712.2028] [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
M. Lemos and P. Liendo, Bootstrapping \( \mathcal{N} \) = 2 chiral correlators, JHEP 01 (2016) 025 [arXiv:1510.03866] [INSPIRE].
M. Lemos and P. Liendo, \( \mathcal{N} \) = 2 central charge bounds from 2d chiral algebras, JHEP 04 (2016) 004 [arXiv:1511.07449] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1601.00011
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Argyres, P.C., Lotito, M., Lü, Y. et al. Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows. J. High Energ. Phys. 2018, 2 (2018). https://doi.org/10.1007/JHEP02(2018)002
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)002