Abstract
We study the algebraic structure of the mesonic moduli spaces of bipartite field theories by computing the Hilbert series. Bipartite field theories form a large family of 4d \( \mathcal{N} \) = 1 supersymmetric gauge theories that are defined by bipartite graphs on Riemann surfaces with boundaries. By calculating the Hilbert series, we are able to identify the generators and defining generator relations of the mesonic moduli spaces of these theories. Moreover, we show that certain bipartite field theories exhibit enhanced global symmetries which can be identified through the computation of the corresponding refined Hilbert series. As part of our study, we introduce two one-parameter families of bipartite field theories defined on cylinders whose mesonic moduli spaces are all complete intersection toric Calabi-Yau 3-folds.
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Acknowledgments
R.-K. S. would like to thank Jiakang Bao, Sebastian Franco, Georgios P. Goulas, Dongwook Ghim, Amihay Hanany, Yang-Hui He, Alessandro Pini and Masahito Yamazaki for discussions and collaborations on related topics. He would also like to thank the Simons Center for Geometry and Physics at Stony Brook University, the Merkin Center for Pure and Applied Mathematics at the California Institute of Technology, the Kavli Institute for the Physics and Mathematics of the University at the University of Tokyo, as well as the Aspen Center for Physics for hospitality during various stages of this work. R.-K. S. is supported by a Basic Research Grant of the National Research Foundation of Korea (NRF-2022R1F1A1073128). He is also supported by a Start-up Research Grant for new faculty at UNIST (1.210139.01) and a UNIST AI Incubator Grant (1.230038.01). He is also partly supported by the BK21 Program (“Next Generation Education Program for Mathematical Sciences”, 4299990414089) funded by the Ministry of Education in Korea and the National Research Foundation of Korea (NRF).
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Kho, M., Seong, RK. Hilbert series of bipartite field theories. J. High Energ. Phys. 2024, 20 (2024). https://doi.org/10.1007/JHEP09(2024)020
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DOI: https://doi.org/10.1007/JHEP09(2024)020