Abstract
Argyres-Douglas theories constitute an important class of superconformal field theories in 4d. The main focus of this paper is on two infinite families of such theories, known as \( {D}_p^b \)(SO(2N)) and (Am, Dn). We analyze in depth their conformal manifolds. In doing so we encounter several theories of class 𝒮 of twisted Aodd, twisted Aeven and twisted D types associated with a sphere with one twisted irregular puncture and one twisted regular puncture. These models include Dp(G) theories, with G non-simply-laced algebras. A number of new properties of such theories are discussed in detail, along with new SCFTs that arise from partially closing the twisted regular puncture. Moreover, we systematically present the 3d mirror theories, also known as the magnetic quivers, for the \( {D}_p^b \)(SO(2N)) theories, with p ≥ b, and the (Am, Dn) theories, with arbitrary m and n. We also discuss the 3d reduction and mirror theories of certain \( {D}_p^b \)(SO(2N)) theories, with p < b, where the former arises from gauging topological symmetries of some \( {T}_p^{\sigma } \)[SO(2M)] theories that are not manifest in the Lagrangian description of the latter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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 [Erratum ibid. 430 (1994) 485] [hep-th/9407087] [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 proceedings of the Conference on the Mathematical Beauty of Physics (In Memory of C. Itzykson), Saclay, France, 5–7 June 1996, pp. 67–82 [hep-th/9607125] [INSPIRE].
A.D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [INSPIRE].
S. Cecotti, A. Neitzke and C. Vafa, R-Twisting and 4d/2d Correspondences, arXiv:1006.3435 [INSPIRE].
G. Bonelli, K. Maruyoshi and A. Tanzini, Wild Quiver Gauge Theories, JHEP 02 (2012) 031 [arXiv:1112.1691] [INSPIRE].
D. Xie, General Argyres-Douglas Theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [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. Gaiotto, N = 2 dualities, JHEP 08 (2012) 034 [arXiv:0904.2715] [INSPIRE].
D. Gaiotto, G.W. Moore and A. Neitzke, Wall-crossing, Hitchin Systems, and the WKB Approximation, arXiv:0907.3987 [INSPIRE].
K.A. Intriligator and N. Seiberg, Mirror symmetry in three-dimensional gauge theories, Phys. Lett. B 387 (1996) 513 [hep-th/9607207] [INSPIRE].
S. Cremonesi, G. Ferlito, A. Hanany and N. Mekareeya, Instanton Operators and the Higgs Branch at Infinite Coupling, JHEP 04 (2017) 042 [arXiv:1505.06302] [INSPIRE].
G. Ferlito, A. Hanany, N. Mekareeya and G. Zafrir, 3d Coulomb branch and 5d Higgs branch at infinite coupling, JHEP 07 (2018) 061 [arXiv:1712.06604] [INSPIRE].
A. Hanany and N. Mekareeya, The small E8 instanton and the Kraft Procesi transition, JHEP 07 (2018) 098 [arXiv:1801.01129] [INSPIRE].
S. Cabrera, A. Hanany and F. Yagi, Tropical Geometry and Five Dimensional Higgs Branches at Infinite Coupling, JHEP 01 (2019) 068 [arXiv:1810.01379] [INSPIRE].
S. Cabrera, A. Hanany and M. Sperling, Magnetic quivers, Higgs branches, and 6d N = (1, 0) theories, JHEP 06 (2019) 071 [Erratum JHEP 07 (2019) 137] [arXiv:1904.12293] [INSPIRE].
Y. Wang and D. Xie, Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d (2, 0) theories, Phys. Rev. D 100 (2019) 025001 [arXiv:1805.08839] [INSPIRE].
D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory Part I: Classification, arXiv:1510.01324 [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].
C. Closset, S. Giacomelli, S. Schäfer-Nameki and Y.-N. Wang, 5d and 4d SCFTs: Canonical Singularities, Trinions and S-Dualities, JHEP 05 (2021) 274 [arXiv:2012.12827] [INSPIRE].
D. Nanopoulos and D. Xie, More Three Dimensional Mirror Pairs, JHEP 05 (2011) 071 [arXiv:1011.1911] [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].
S. Giacomelli, RG flows with supersymmetry enhancement and geometric engineering, JHEP 06 (2018) 156 [arXiv:1710.06469] [INSPIRE].
F. Aprile, S. Pasquetti and Y. Zenkevich, Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles, JHEP 04 (2019) 138 [arXiv:1812.08142] [INSPIRE].
D. Gaiotto and E. Witten, S-duality of Boundary Conditions In N = 4 Super Yang-Mills Theory, Adv. Theor. Math. Phys. 13 (2009) 721 [arXiv:0807.3720] [INSPIRE].
J.A. Minahan and D. Nemeschansky, Superconformal fixed points with En global symmetry, Nucl. Phys. B 489 (1997) 24 [hep-th/9610076] [INSPIRE].
F. Carta and A. Mininno, No go for a flow, JHEP 05 (2020) 108 [arXiv:2002.07816] [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 1, hep-th/9809187 [INSPIRE].
R. Gopakumar and C. Vafa, M theory and topological strings. 2, hep-th/9812127 [INSPIRE].
R. Gopakumar and C. Vafa, On the gauge theory/geometry correspondence, in AMS/IP Studies in Advanced Mathematics 23, American Mathematical Society/International Press (2001), pp. 45–63 [Adv. Theor. Math. Phys. 3 (1999) 1415] [hep-th/9811131] [INSPIRE].
S. Cecotti, M. Del Zotto and S. Giacomelli, More on the N = 2 superconformal systems of type Dp(G), JHEP 04 (2013) 153 [arXiv:1303.3149] [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].
O. Aharony and Y. Tachikawa, S-folds and 4d N = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
E. Witten, An SU(2) Anomaly, Phys. Lett. B 117 (1982) 324 [INSPIRE].
Y. Tachikawa, Y. Wang and G. Zafrir, Comments on the twisted punctures of Aeven class S theory, JHEP 06 (2018) 163 [arXiv:1804.09143] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Gaiotto duality for the twisted A2N−1 series, JHEP 05 (2015) 075 [arXiv:1212.3952] [INSPIRE].
O. Chacaltana, J. Distler and A. Trimm, Tinkertoys for the Twisted D-Series, JHEP 04 (2015) 173 [arXiv:1309.2299] [INSPIRE].
C. Beem and W. Peelaers, Argyres-Douglas Theories in Class S Without Irregularity, arXiv:2005.12282 [INSPIRE].
E. Beratto, S. Giacomelli, N. Mekareeya and M. Sacchi, 3d mirrors of the circle reduction of twisted A2N theories of class S, JHEP 09 (2020) 161 [arXiv:2007.05019] [INSPIRE].
O. Chacaltana, J. Distler and Y. Tachikawa, Nilpotent orbits and codimension-two defects of 6d N = (2, 0) theories, Int. J. Mod. Phys. A 28 (2013) 1340006 [arXiv:1203.2930] [INSPIRE].
Y. Tachikawa and S. Terashima, Seiberg-Witten Geometries Revisited, JHEP 09 (2011) 010 [arXiv:1108.2315] [INSPIRE].
P. Agarwal, I. Bah, K. Maruyoshi and J. Song, Quiver tails and \( \mathcal{N} \) = 1 SCFTs from M 5-branes, JHEP 03 (2015) 049 [arXiv:1409.1908] [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 JHEP 04 (2017) 113] [arXiv:1610.05311] [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].
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].
C. Hwang, S. Pasquetti and M. Sacchi, 4d mirror-like dualities, JHEP 09 (2020) 047 [arXiv:2002.12897] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, \( {T}_{\rho}^{\sigma } \)(G) theories and their Hilbert series, JHEP 01 (2015) 150 [arXiv:1410.1548] [INSPIRE].
S. Giacomelli and N. Mekareeya, Mirror theories of 3d \( \mathcal{N} \) = 2 SQCD, JHEP 03 (2018) 126 [arXiv:1711.11525] [INSPIRE].
D. Xie, M5 brane and four dimensional N = 1 theories I, JHEP 04 (2014) 154 [arXiv:1307.5877] [INSPIRE].
A. Dey, Three Dimensional Mirror Symmetry beyond ADE quivers and Argyres-Douglas theories, arXiv:2004.09738 [INSPIRE].
M. Buican and T. Nishinaka, Conformal Manifolds in Four Dimensions and Chiral Algebras, J. Phys. A 49 (2016) 465401 [arXiv:1603.00887] [INSPIRE].
C. Closset, S. Schäfer-Nameki and Y.-N. Wang, Coulomb and Higgs Branches from Canonical Singularities: Part 0, JHEP 02 (2021) 003 [arXiv:2007.15600] [INSPIRE].
O. Aharony, N. Seiberg and Y. Tachikawa, Reading between the lines of four-dimensional gauge theories, JHEP 08 (2013) 115 [arXiv:1305.0318] [INSPIRE].
M. Del Zotto, I. García Etxebarria and S.S. Hosseini, Higher form symmetries of Argyres-Douglas theories, JHEP 10 (2020) 056 [arXiv:2007.15603] [INSPIRE].
A. Bourget, J.F. Grimminger, A. Hanany, R. Kalveks, M. Sperling and Z. Zhong, Magnetic Lattices for Orthosymplectic Quivers, JHEP 12 (2020) 092 [arXiv:2007.04667] [INSPIRE].
S. Benvenuti, A. Hanany and N. Mekareeya, The Hilbert Series of the One Instanton Moduli Space, JHEP 06 (2010) 100 [arXiv:1005.3026] [INSPIRE].
P.C. Argyres and N. Seiberg, S-duality in N = 2 supersymmetric gauge theories, JHEP 12 (2007) 088 [arXiv:0711.0054] [INSPIRE].
A. Bourget, A. Dancer, J.F. Grimminger, A. Hanany, F. Kirwan and Z. Zhong, Orthosymplectic Implosions, arXiv:2103.05458 [INSPIRE].
F. Benini, Y. Tachikawa and D. Xie, Mirrors of 3d Sicilian theories, JHEP 09 (2010) 063 [arXiv:1007.0992] [INSPIRE].
S. Cremonesi, A. Hanany and A. Zaffaroni, Monopole operators and Hilbert series of Coulomb branches of 3d \( \mathcal{N} \) = 4 gauge theories, JHEP 01 (2014) 005 [arXiv:1309.2657] [INSPIRE].
S.S. Razamat and B. Willett, Down the rabbit hole with theories of class \( \mathcal{S} \), JHEP 10 (2014) 099 [arXiv:1403.6107] [INSPIRE].
M. Fazzi, A. Lanir, S.S. Razamat and O. Sela, Chiral 3d SU(3) SQCD and \( \mathcal{N} \) = 2 mirror duality, JHEP 11 (2018) 025 [arXiv:1808.04173] [INSPIRE].
A. Hanany and N. Mekareeya, Complete Intersection Moduli Spaces in N = 4 Gauge Theories in Three Dimensions, JHEP 01 (2012) 079 [arXiv:1110.6203] [INSPIRE].
A. Kapustin, Dn quivers from branes, JHEP 12 (1998) 015 [hep-th/9806238] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Hall-Littlewood polynomials, JHEP 09 (2014) 178 [arXiv:1403.0585] [INSPIRE].
S. Cremonesi, A. Hanany, N. Mekareeya and A. Zaffaroni, Coulomb branch Hilbert series and Three Dimensional Sicilian Theories, JHEP 09 (2014) 185 [arXiv:1403.2384] [INSPIRE].
A. Collinucci, A. Sangiovanni and R. Valandro, Genus zero Gopakumar-Vafa invariants from open strings, arXiv:2104.14493 [INSPIRE].
A. Collinucci, M. De Marco, A. Sangiovanni and R. Valandro, Higgs branches of 5d rank-zero theories from geometry, arXiv:2105.12177 [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: 2105.08064
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
Carta, F., Giacomelli, S., Mekareeya, N. et al. Conformal manifolds and 3d mirrors of Argyres-Douglas theories. J. High Energ. Phys. 2021, 15 (2021). https://doi.org/10.1007/JHEP08(2021)015
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2021)015