Abstract
We study 3D \( \mathcal{N} \) = 2 supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D \( \mathcal{N} \) = 2 theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate ℙ1-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed “flavor symmetry duality”. Many examples are analyzed with an emphasis on toric CY4s and ℂ4 orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D \( \mathcal{N} \) = 2 theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in ℝ3 can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D \( \mathcal{N} \) = 2 theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.
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Acknowledgments
We thank Bobby Acharya, Shi Cheng, Cyril Closset, Xin Gao, Amihay Hanany, Chiung Hwang, Yukari Ito, Qiang Jia, Hee-Cheol Kim, Sung-Soo Kim, Osama Khlaif, Kimyeong Lee, Linfeng Li, Hong Lu, Ruben Minasian, Sakura Schafer-Nameki, Benjamin Sung, Xin Wang, Dan Xie and Yi Zhang for discussions. JT would like to thank Ying Zhang for her love and support. JT would like to thank the organizers of “Seventh Annual Meeting of Simons Collaboration on Special Holonomy in Geometry, Analysis, and Physics” and “Special Holonomy: Progress and Open Problems 2023” for the invitation and hospitality. YNW would like to thank the organizers of “2023 East Asia Joint Workshop on Fields and Strings” at Xi’an for the invitation and hospitality. JT and YNW would like to thank the organizers of “McKay correspondence, Tilting theory and related topics” at IPMU for the invitation and hospitality. JT is supported in part by a grant from the Simons Foundation (#488569, Bobby Acharya). MN and YNW are supported by National Natural Science Foundation of China under Grant No. 12175004, by Peking University under startup Grant No. 7100603667 and by Young Elite Scientists Sponsorship Program by CAST (2022QNRC001, 2023QNRC001).
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Najjar, M., Tian, J. & Wang, YN. 3d \( \mathcal{N} \) = 2 theories from M-theory on CY4 and IIB brane box. J. High Energ. Phys. 2024, 38 (2024). https://doi.org/10.1007/JHEP05(2024)038
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DOI: https://doi.org/10.1007/JHEP05(2024)038