Abstract
Six-dimensional superconformal field theories (SCFTs) have an atomic classification in terms of elementary building blocks, conformal systems that generalize matter and can be fused together to form all known 6d SCFTs in terms of generalized 6d quivers. It is therefore natural to ask whether 5d SCFTs can be organized in a similar manner, as the outcome of fusions of certain elementary building blocks, which we call 5d conformal matter theories. In this project we begin exploring this idea and we give a systematic construction of 5d generalized “bifundamental” SCFTs, building from geometric engineering techniques in M-theory. In particular, we find several examples of (\( {\mathfrak{e}}_6 \), \( {\mathfrak{e}}_6 \)), (\( {\mathfrak{e}}_7 \), \( {\mathfrak{e}}_7 \)) and (\( {\mathfrak{e}}_8 \), \( {\mathfrak{e}}_8 \)) 5d bifundamental SCFTs beyond the ones arising from (elementary) KK reductions of the 6d conformal matter theories. We show that these can be fused together giving rise to 5d SCFTs captured by 5d generalized linear quivers with exceptional gauge groups as nodes, and links given by 5d conformal matter. As a first application of these models we uncover a large class of novel 5d dualites, that generalize the well-known fiber/base dualities outside the toric realm.
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08 August 2024
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP08(2024)067
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Acknowledgments
MDZ thanks David R. Morrison and Jonathan J. Heckman for several illuminating discussions in the period 2015-17 which inspired this work, as well as the Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics for many inspiring discussions in the period 2018-2020, which served as further motivation for this paper. We thank Bobby Acharya, Sergio Benvenuti, Amihay Hanany, Lotte Hollands, Marco Fazzi, Alessandro Tomasiello, Sakura Schäfer-Nameki and Roberto Valandro for discussions. The work of MDZ and MDM has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 851931). MDZ also acknowledges support from the Simons Foundation Grant #888984 (Simons Collaboration on Global Categorical Symmetries). AS wishes to thank Accademia dei Lincei for financial support, as well as the Department of Mathematics and the Department of Physics of Uppsala University for hospitality during the realization of this work. AS further acknowledges funding from the Simons Collaboration on Special Holonomy. MDM thanks the “Fondazione Angelo Della Riccia” for financial support and acknowledges the kind hospitality of the Department of Mathematics of Uppsala University during the realization of this work. MG was partially supported by the project PRIN 2020 “Squarefree Gröbner degenerations, special varieties and related topics” (MUR, project number 2020355B8Y). MDZ thanks the organizers of the XIII Workshop on Geometric Correspondences of Gauge Theories, held at the Insitute for Geometry and Physics in Trieste, Italy, in June 2023 as well as the SwissMap research station in Les Diableret for hospitality during the completion of this work.
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De Marco, M., Del Zotto, M., Graffeo, M. et al. Conformal matter. J. High Energ. Phys. 2024, 306 (2024). https://doi.org/10.1007/JHEP05(2024)306
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DOI: https://doi.org/10.1007/JHEP05(2024)306