Abstract
We determine all 5d SCFTs upto rank three by studying RG flows of 5d KK theories. Our analysis reveals the existence of new rank one and rank two 5d SCFTs not captured by previous classifications. In addition to that, we provide for the first time a systematic and conjecturally complete classification of rank three 5d SCFTs. Our methods are based on a recently studied geometric description of 5d KK theories, thus demonstrating the utility of these geometric descriptions. It is straightforward, though computationally intensive, to extend this work and systematically classify 5d SCFTs of higher ranks (greater than or equal to four) by using the geometric description of 5d KK theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.J. Heckman, D.R. Morrison and C. Vafa, On the Classification of 6D SCFTs and Generalized ADE Orbifolds, JHEP 05 (2014) 028 [Erratum ibid. 06 (2015) 017] [arXiv:1312.5746] [INSPIRE].
J.J. Heckman, D.R. Morrison, T. Rudelius and C. Vafa, Atomic Classification of 6D SCFTs, Fortsch. Phys. 63 (2015) 468 [arXiv:1502.05405] [INSPIRE].
L. Bhardwaj, Classification of 6d \( \mathcal{N} \) = (1, 0) gauge theories, JHEP 11 (2015) 002 [arXiv:1502.06594] [INSPIRE].
L. Bhardwaj, Revisiting the classifications of 6d SCFTs and LSTs, JHEP 03 (2020) 171 [arXiv:1903.10503] [INSPIRE].
M. Del Zotto, J.J. Heckman and D.R. Morrison, 6D SCFTs and Phases of 5D Theories, JHEP 09 (2017) 147 [arXiv:1703.02981] [INSPIRE].
D. Xie and S.-T. Yau, Three dimensional canonical singularity and five dimensional \( \mathcal{N} \) = 1 SCFT, JHEP 06 (2017) 134 [arXiv:1704.00799] [INSPIRE].
P. Jefferson, H.-C. Kim, C. Vafa and G. Zafrir, Towards Classification of 5d SCFTs: Single Gauge Node, arXiv:1705.05836 [INSPIRE].
P. Jefferson, S. Katz, H.-C. Kim and C. Vafa, On Geometric Classification of 5d SCFTs, JHEP 04 (2018) 103 [arXiv:1801.04036] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Rank one, JHEP 07 (2019) 178 [Addendum ibid. 01 (2020) 153] [arXiv:1809.01650] [INSPIRE].
L. Bhardwaj and P. Jefferson, Classifying 5d SCFTs via 6d SCFTs: Arbitrary rank, JHEP 10 (2019) 282 [arXiv:1811.10616] [INSPIRE].
F. Apruzzi, L. Lin and C. Mayrhofer, Phases of 5d SCFTs from M-/F-theory on Non-Flat Fibrations, JHEP 05 (2019) 187 [arXiv:1811.12400] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, 5d Superconformal Field Theories and Graphs, Phys. Lett. B 800 (2020) 135077 [arXiv:1906.11820] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States, JHEP 11 (2019) 068 [arXiv:1907.05404] [INSPIRE].
F. Apruzzi, C. Lawrie, L. Lin, S. Schäfer-Nameki and Y.-N. Wang, Fibers add Flavor, Part II: 5d SCFTs, Gauge Theories, and Dualities, JHEP 03 (2020) 052 [arXiv:1909.09128] [INSPIRE].
L. Bhardwaj, P. Jefferson, H.-C. Kim, H.-C. Tarazi and C. Vafa, Twisted Circle Compactifications of 6d SCFTs, arXiv:1909.11666 [INSPIRE].
C. Closset, M. Del Zotto and V. Saxena, Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective, SciPost Phys. 6 (2019) 052 [arXiv:1812.10451] [INSPIRE].
L. Bhardwaj, D.R. Morrison, Y. Tachikawa and A. Tomasiello, The frozen phase of F-theory, JHEP 08 (2018) 138 [arXiv:1805.09070] [INSPIRE].
E. Witten, Toroidal compactification without vector structure, JHEP 02 (1998) 006 [hep-th/9712028] [INSPIRE].
J. de Boer et al., Triples, fluxes, and strings, Adv. Theor. Math. Phys. 4 (2002) 995 [hep-th/0103170] [INSPIRE].
Y. Tachikawa, Frozen singularities in M and F-theory, JHEP 06 (2016) 128 [arXiv:1508.06679] [INSPIRE].
K. Ohmori, H. Shimizu, Y. Tachikawa and K. Yonekura, 6d \( \mathcal{N} \) = (1, 0) theories on S1/T 2 and class S theories: part II, JHEP 12 (2015) 131 [arXiv:1508.00915] [INSPIRE].
Y. Tachikawa, On S-duality of 5d super Yang-Mills on S1 , JHEP 11 (2011) 123 [arXiv:1110.0531] [INSPIRE].
L. Bhardwaj, Dualities of 5d gauge theories from S-duality, JHEP 07 (2020) 012 [arXiv:1909.05250] [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: 1909.09635
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
Bhardwaj, L. On the classification of 5d SCFTs. J. High Energ. Phys. 2020, 7 (2020). https://doi.org/10.1007/JHEP09(2020)007
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2020)007