Abstract
We systematically study 4D \( \mathcal{N} \) = 2 superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in ℂ4. We show that if a theory in this class has no \( \mathcal{N} \) = 2-preserving exactly marginal deformation (i.e., the theory is isolated as an \( \mathcal{N} \) = 2 SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the a and c central charges, this condition implies that IHS theories satisfying \( a<\frac{1}{24}\left(15r+2f\right) \) and \( c<\frac{1}{6}\left(3r+f\right) \) (where r is the complex dimension of the Coulomb branch, and f is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D \( \mathcal{N} \) = 2 SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Cecotti, A. Neitzke and C. Vafa, R-twisting and 4d/2d correspondences, arXiv:1006.3435 [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].
N. Nekrasov, BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters, JHEP 03 (2016) 181 [arXiv:1512.05388] [INSPIRE].
R. Donagi and E. Witten, Supersymmetric Yang-Mills theory and integrable systems, Nucl. Phys. B 460 (1996) 299 [hep-th/9510101] [INSPIRE].
D. Gaiotto, L. Rastelli and S. S. Razamat, Bootstrapping the superconformal index with surface defects, JHEP 01 (2013) 022 [arXiv:1207.3577] [INSPIRE].
K. Papadodimas, Topological anti-topological fusion in four-dimensional superconformal field theories, JHEP 08 (2010) 118 [arXiv:0910.4963] [INSPIRE].
E. Gerchkovitz, J. Gomis and Z. Komargodski, Sphere partition functions and the Zamolodchikov metric, JHEP 11 (2014) 001 [arXiv:1405.7271] [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].
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 N. Seiberg, The moduli space of vacua of N = 2 SUSY QCD and duality in N = 1 SUSY QCD, Nucl. Phys. B 471 (1996) 159 [hep-th/9603042] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part I. Physical constraints on relevant deformations, JHEP 02 (2018) 001 [arXiv:1505.04814] [INSPIRE].
P. C. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part II. Construction of special Kähler geometries and RG flows, JHEP 02 (2018) 002 [arXiv:1601.00011] [INSPIRE].
P. Argyres, M. Lotito, Y. Lü and M. Martone, Geometric constraints on the space of \( \mathcal{N} \) = 2 SCFTs. Part III. Enhanced Coulomb branches and central charges, JHEP 02 (2018) 003 [arXiv:1609.04404] [INSPIRE].
A. Bourget et al., The Higgs mechanism — Hasse diagrams for symplectic singularities, JHEP 01 (2020) 157 [arXiv:1908.04245] [INSPIRE].
M. Buican and T. Nishinaka, Conformal manifolds in four dimensions and chiral algebras, J. Phys. A 49 (2016) 465401 [arXiv:1603.00887] [INSPIRE].
D. Gaiotto, A. Kapustin, N. Seiberg and B. Willett, Generalized global symmetries, JHEP 02 (2015) 172 [arXiv:1412.5148] [INSPIRE].
M. Buican, Z. Laczko and T. Nishinaka, Flowing from 16 to 32 supercharges, JHEP 10 (2018) 175 [arXiv:1807.02785] [INSPIRE].
M. Buican, L. Li and T. Nishinaka, Peculiar index relations, 2D TQFT, and universality of SUSY enhancement, JHEP 01 (2020) 187 [arXiv:1907.01579] [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].
E. Perlmutter, L. Rastelli, C. Vafa and I. Valenzuela, A CFT Distance Conjecture, arXiv:2011.10040 [INSPIRE].
A. D. Shapere and C. Vafa, BPS structure of Argyres-Douglas superconformal theories, hep-th/9910182 [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].
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].
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].
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].
S. S.-T. Yau and Y. Yu, Classification of 3-dimensional isolated rational hypersurface singularities with c∗-action, Rocky Mountain J. Math. 35 (2005) 1795.
D. Xie and S.-T. Yau, 4d N = 2 SCFT and singularity theory. Part I: classification, arXiv:1510.01324 [INSPIRE].
I. C. Davenport and I. V. Melnikov, Landau-Ginzburg skeletons, JHEP 05 (2017) 050 [arXiv:1608.04259] [INSPIRE].
S. Hellerman, A. Henriques, T. Pantev, E. Sharpe and M. Ando, Cluster decomposition, T-duality, and gerby CFT’s, Adv. Theor. Math. Phys. 11 (2007) 751 [hep-th/0606034] [INSPIRE].
Decomposition 2021, May 22–23, online, https://indico.phys.vt.edu/event/46/ (2021).
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].
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 Dp (G), JHEP 04 (2013) 153 [arXiv:1303.3149] [INSPIRE].
S. S. Hosseini and R. Moscrop, Maruyoshi-Song flows and defect groups of \( {D}_p^b \) (G) theories, JHEP 10 (2021) 119 [arXiv:2106.03878] [INSPIRE].
Y. Tachikawa, On the 6d origin of discrete additional data of 4d gauge theories, JHEP 05 (2014) 020 [arXiv:1309.0697] [INSPIRE].
S. Gukov, P.-S. Hsin and D. Pei, Generalized global symmetries of T[M] theories. Part I, JHEP 04 (2021) 232 [arXiv:2010.15890] [INSPIRE].
L. Bhardwaj, M. Hubner and S. Schäfer-Nameki, 1-form symmetries of 4d N = 2 class S theories, SciPost Phys. 11 (2021) 096 [arXiv:2102.01693] [INSPIRE].
O. Aharony and Y. Tachikawa, S-folds and 4d N = 3 superconformal field theories, JHEP 06 (2016) 044 [arXiv:1602.08638] [INSPIRE].
G. Zafrir, An \( \mathcal{N} \) = 1 Lagrangian for an \( \mathcal{N} \) = 3 SCFT, JHEP 01 (2021) 062 [arXiv:2007.14955] [INSPIRE].
O. Aharony and M. Evtikhiev, On four dimensional N = 3 superconformal theories, JHEP 04 (2016) 040 [arXiv:1512.03524] [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].
D. Xie and S.-T. Yau, Semicontinuity of 4d N = 2 spectrum under renormalization group flow, JHEP 03 (2016) 094 [arXiv:1510.06036] [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].
C. P. Boyer, K. Galicki and S. R. Simanca, The Sasaki cone and extremal Sasakian metrics, in Riemannian topology and geometric structures on manifolds, K. Galicki and S.R. Simanca eds., Springer (2009).
M. Buican, Minimal distances between scfts, JHEP 01 (2014) 155 [arXiv:1311.1276] [INSPIRE].
M. Buican, T. Nishinaka and C. Papageorgakis, Constraints on chiral operators in \( \mathcal{N} \) = 2 SCFTs, JHEP 12 (2014) 095 [arXiv:1407.2835] [INSPIRE].
D. Green, Z. Komargodski, N. Seiberg, Y. Tachikawa and B. Wecht, Exactly marginal deformations and global symmetries, JHEP 06 (2010) 106 [arXiv:1005.3546] [INSPIRE].
M. Buican, Minimal Distances between SCFTs, talk given at Quantum Fields Beyond Perturbation Theory, January 27–31, KITP, U.S.A. (2014).
F. Carta, S. Giacomelli, N. Mekareeya and A. Mininno, Conformal manifolds and 3d mirrors of Argyres-Douglas theories, JHEP 08 (2021) 015 [arXiv:2105.08064] [INSPIRE].
M. Del Zotto, C. Vafa and D. Xie, Geometric engineering, mirror symmetry and 6d(1,0) → \( 4{d}_{\left(\mathcal{N}=2\right)} \), JHEP 11 (2015) 123 [arXiv:1504.08348] [INSPIRE].
M. Buican and T. Nishinaka, \( \mathcal{N} \) = 4 SYM, Argyres-Douglas Theories, and an Exact Graded Vector Space Isomorphism, arXiv:2012.13209 [INSPIRE].
L. Bhardwaj, Global form of flavor symmetry groups in 4d N = 2 theories of class S, arXiv:2105.08730 [INSPIRE].
F. Apruzzi, L. Bhardwaj, J. Oh and S. Schäfer-Nameki, The global form of flavor symmetries and 2-group symmetries in 5d SCFTs, arXiv:2105.08724 [INSPIRE].
M. Buican and T. Nishinaka, On the superconformal index of Argyres-Douglas theories, J. Phys. A 49 (2016) 015401 [arXiv:1505.05884] [INSPIRE].
M. Buican and T. Nishinaka, Argyres-Douglas theories, the Macdonald index, and an RG inequality, JHEP 02 (2016) 159 [arXiv:1509.05402] [INSPIRE].
D. Xie, General Argyres-Douglas theory, JHEP 01 (2013) 100 [arXiv:1204.2270] [INSPIRE].
M. Buican and T. Nishinaka, Argyres-Douglas theories, S1 reductions, and topological symmetries, J. Phys. A 49 (2016) 045401 [arXiv:1505.06205] [INSPIRE].
W. Nahm, Supersymmetries and their representations, Nucl. Phys. B 135 (1978) 149 [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].
S. Giacomelli, RG flows with supersymmetry enhancement and geometric engineering, JHEP 06 (2018) 156 [arXiv:1710.06469] [INSPIRE].
Y. Wang and D. Xie, Classification of Argyres-Douglas theories from M5 branes, Phys. Rev. D 94 (2016) 065012 [arXiv:1509.00847] [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].
J. Chen, On exact correlation functions of chiral ring operators in 2d \( \mathcal{N} \) = (2, 2) SCFTs via localization, JHEP 03 (2018) 065 [arXiv:1712.01164] [INSPIRE].
P. C. Argyres and M. Martone, 4d \( \mathcal{N} \) = 2 theories with disconnected gauge groups, JHEP 03 (2017) 145 [arXiv:1611.08602] [INSPIRE].
T. Nishinaka and Y. Tachikawa, On 4d rank-one \( \mathcal{N} \) = 3 superconformal field theories, JHEP 09 (2016) 116 [arXiv:1602.01503] [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].
Y. Tanizaki and M. Ünsal, Modified instanton sum in QCD and higher-groups, JHEP 03 (2020) 123 [arXiv:1912.01033] [INSPIRE].
B. Heidenreich, J. McNamara, M. Montero, M. Reece, T. Rudelius and I. Valenzuela, Non-invertible global symmetries and completeness of the spectrum, JHEP 09 (2021) 203 [arXiv:2104.07036] [INSPIRE].
M. Kreuzer and H. Skarke, No mirror symmetry in Landau-Ginzburg spectra!, Nucl. Phys. B 388 (1992) 113 [hep-th/9205004] [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: 2106.09807
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
Buican, M., Jiang, H. 1-form symmetry, isolated \( \mathcal{N} \) = 2 SCFTs, and Calabi-Yau threefolds. J. High Energ. Phys. 2021, 24 (2021). https://doi.org/10.1007/JHEP12(2021)024
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2021)024