Abstract
In this paper we study a class of \( \mathcal{N}=2 \) SCFTs with ADE global symmetry defined via Type IIB compactification on a class of hypersurfaces in ℂ3 × ℂ*. These can also be constructed by compactifying the 6d (2,0) theory of type ADE on a sphere with an irregular and a full punctures. When we couple to the ADE moment map a chiral multiplet in the adjoint representation and turn on a (principal) nilpotent vev for it, all the theories in this family display enhancement of supersymmetry in the infrared. We observe that all known examples of theories which flow, upon the same type of deformation, to strongly coupled \( \mathcal{N}=2 \) theories fit naturally in our framework, thus providing a new perspective on this topic. We propose an infrared equivalence between this RG flow and a manifestly \( \mathcal{N}=2 \) preserving one and, as a byproduct, we extract a precise prescription to relate the SW curves describing the UV and IR fixed points for all theories with A or D global symmetry. We also find, for a certain subclass, a simple relation between UV and IR theories at the level of chiral algebras.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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].
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].
T. Eguchi and K. Hori, N = 2 superconformal field theories in four-dimensions and A-D-E classification, in The mathematical beauty of physics: A memorial volume for Claude Itzykson. Proceedings, Conference, Saclay, France, June 5–7, 1996, pp. 67–82 [hep-th/9607125] [INSPIRE].
D. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
K. Maruyoshi and J. Song, Enhancement of Supersymmetry via Renormalization Group Flow and the Superconformal Index, Phys. Rev. Lett. 118 (2017) 151602 [arXiv:1606.05632] [INSPIRE].
K. Maruyoshi and J. Song, \( \mathcal{N}=1 \) deformations and RG flows of \( \mathcal{N}=2 \) SCFTs, JHEP 02 (2017) 075 [arXiv:1607.04281] [INSPIRE].
P. Agarwal, K. Maruyoshi and J. Song, \( \mathcal{N}=1 \) Deformations and RG flows of \( \mathcal{N}=2 \) SCFTs, part II: non-principal deformations, JHEP 12 (2016) 103 [Addendum ibid. 04 (2017) 113] [arXiv:1610.05311] [INSPIRE].
A. Gadde, S.S. Razamat and B. Willett, ”Lagrangian” for a Non-Lagrangian Field Theory with \( \mathcal{N}=2 \) Supersymmetry, Phys. Rev. Lett. 115 (2015) 171604 [arXiv:1505.05834] [INSPIRE].
S. Benvenuti and S. Giacomelli, Supersymmetric gauge theories with decoupled operators and chiral ring stability, Phys. Rev. Lett. 119 (2017) 251601 [arXiv:1706.02225] [INSPIRE].
S. Benvenuti and S. Giacomelli, Abelianization and sequential confinement in 2 + 1 dimensions, JHEP 10 (2017) 173 [arXiv:1706.04949] [INSPIRE].
S. Benvenuti and S. Giacomelli, Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 106 [arXiv:1707.05113] [INSPIRE].
K.A. Intriligator and B. Wecht, The exact superconformal R symmetry maximizes a, Nucl. Phys. B 667 (2003) 183 [hep-th/0304128] [INSPIRE].
M. Evtikhiev, Studying superconformal symmetry enhancement through indices, JHEP 04 (2018) 120 [arXiv:1708.08307] [INSPIRE].
Y. Wang and D. Xie, Classification of Argyres-Douglas theories from M5 branes, Phys. Rev. D 94 (2016) 065012 [arXiv:1509.00847] [INSPIRE].
D. Xie, General Argyres-Douglas Theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
S. Cecotti and M. Del Zotto, Infinitely many N = 2 SCFT with ADE flavor symmetry, JHEP 01 (2013) 191 [arXiv:1210.2886] [INSPIRE].
S. Cecotti, M. Del Zotto and S. Giacomelli, More on the N = 2 superconformal systems of type D p(G), JHEP 04 (2013) 153 [arXiv:1303.3149] [INSPIRE].
C. Beem, M. Lemos, P. Liendo, W. Peelaers, L. Rastelli and B.C. van Rees, Infinite Chiral Symmetry in Four Dimensions, Commun. Math. Phys. 336 (2015) 1359 [arXiv:1312.5344] [INSPIRE].
P. Agarwal, A. Sciarappa and J. Song, \( \mathcal{N}=1 \) Lagrangians for generalized Argyres-Douglas theories, JHEP 10 (2017) 211 [arXiv:1707.04751] [INSPIRE].
D. Xie, W. Yan and S.-T. Yau, Chiral algebra of Argyres-Douglas theory from M5 brane, arXiv:1604.02155 [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-Twisting and 4d/2d Correspondences, arXiv:1006.3435 [INSPIRE].
A.D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE].
D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory Part I: Classification, arXiv:1510.01324 [INSPIRE].
A.D. Shapere and Y. Tachikawa, Central charges of N = 2 superconformal field theories in four dimensions, JHEP 09 (2008) 109 [arXiv:0804.1957] [INSPIRE].
Y. Tachikawa and S. Terashima, Seiberg-Witten Geometries Revisited, JHEP 09 (2011) 010 [arXiv:1108.2315] [INSPIRE].
W. Lerche and N.P. Warner, Exceptional SW geometry from ALE fibrations, Phys. Lett. B 423 (1998) 79 [hep-th/9608183] [INSPIRE].
A. Brandhuber and K. Landsteiner, On the monodromies of N = 2 supersymmetric Yang-Mills theory with gauge group SO(2N), Phys. Lett. B 358 (1995) 73 [hep-th/9507008] [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. Song, D. Xie and W. Yan, Vertex operator algebras of Argyres-Douglas theories from M5-branes, JHEP 12 (2017) 123 [arXiv:1706.01607] [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].
O. Chacaltana, J. Distler, A. Trimm and Y. Zhu, Tinkertoys for the E 7 Theory, arXiv:1704.07890 [INSPIRE].
E. Witten, Solutions of four-dimensional field theories via M-theory, Nucl. Phys. B 500 (1997) 3 [hep-th/9703166] [INSPIRE].
K. Landsteiner, E. Lopez and D.A. Lowe, N = 2 supersymmetric gauge theories, branes and orientifolds, Nucl. Phys. B 507 (1997) 197 [hep-th/9705199] [INSPIRE].
M. Buican, S. Giacomelli, T. Nishinaka and C. Papageorgakis, Argyres-Douglas Theories and S-duality, JHEP 02 (2015) 185 [arXiv:1411.6026] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N}=\left(1,0\right) \) theories on T 2 and class S theories: Part I, JHEP 07 (2015) 014 [arXiv:1503.06217] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, Anomaly polynomial of general 6d SCFTs, PTEP 2014 (2014) 103B07 [arXiv:1408.5572] [INSPIRE].
M. Del Zotto, J.J. Heckman, A. Tomasiello and C. Vafa, 6d Conformal Matter, JHEP 02 (2015) 054 [arXiv:1407.6359] [INSPIRE].
S. Cecotti and M. Del Zotto, On Arnold’s 14 ‘exceptional’ N = 2 superconformal gauge theories, JHEP 10 (2011) 099 [arXiv:1107.5747] [INSPIRE].
C. Beem and L. Rastelli, Vertex operator algebras, Higgs branches and modular differential equations, arXiv:1707.07679 [INSPIRE].
T. Creutzig, W-algebras for Argyres-Douglas theories, arXiv:1701.05926 [INSPIRE].
M. Buican and T. Nishinaka, On the superconformal index of Argyres-Douglas theories, J. Phys. A 49 (2016) 015401 [arXiv:1505.05884] [INSPIRE].
C. Cordova and S.-H. Shao, Schur Indices, BPS Particles and Argyres-Douglas Theories, JHEP 01 (2016) 040 [arXiv:1506.00265] [INSPIRE].
L. Rastelli, Infinite Chiral Symmetry in Four and Six Dimensions, seminar at Harvard University, November 2014.
M. Buican, Z. Laczko and T. Nishinaka, \( \mathcal{N}=2 \) S-duality revisited, JHEP 09 (2017) 087 [arXiv:1706.03797] [INSPIRE].
A. Gadde, K. Maruyoshi, Y. Tachikawa and W. Yan, New N = 1 Dualities, JHEP 06 (2013) 056 [arXiv:1303.0836] [INSPIRE].
P. Agarwal, I. Bah, K. Maruyoshi and J. Song, Quiver tails and \( \mathcal{N}=1 \) SCFTs from M5-branes, JHEP 03 (2015) 049 [arXiv:1409.1908] [INSPIRE].
Y. Tachikawa, A review of the T N theory and its cousins, PTEP 2015 (2015) 11B102 [arXiv:1504.01481] [INSPIRE].
D.I. Panyushev, On the Dynkin index of a principal sl 2 -subalgebra, arXiv:0903.0398.
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: 1710.06469
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Giacomelli, S. RG flows with supersymmetry enhancement and geometric engineering. J. High Energ. Phys. 2018, 156 (2018). https://doi.org/10.1007/JHEP06(2018)156
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP06(2018)156