Abstract
We systematically study the master space of brane brick models that represent a large class of 2d (0, 2) quiver gauge theories. These 2d (0, 2) theories are worldvolume theories of D1-branes that probe singular toric Calabi-Yau 4-folds. The master space is the freely generated space of chiral fields subject to the J- and E-terms and the non-abelian part of the gauge symmetry. We investigate several properties of the master space for abelian brane brick models with U(1) gauge groups. For example, we calculate the Hilbert series, which allows us by using the plethystic programme to identify the generators and defining relations of the master space. By studying several explicit examples, we also show that the Hilbert series of the master space can be expressed in terms of characters of irreducible representations of the full global symmetry of the master space.
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Acknowledgments
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), a UNIST AI Incubator Grant (1.230038.01) and UNIST UBSI Grants (1.220123.01, 1.230065.01), as well as an Industry Research Project (2.220916.01) funded by Samsung SDS in Korea. 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). R.-K. S. is grateful to Per Berglund, Sebastian Franco, Dongwook Ghim, Amihay Hanany, Yang-Hui He and Sangmin Lee for discussions on related topics. He is also grateful to the Simons Center for Geometry and Physics at Stony Brook University for hospitality during the final stages of this work.
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Kho, M., Seong, RK. On the master space for brane brick models. J. High Energ. Phys. 2023, 150 (2023). https://doi.org/10.1007/JHEP09(2023)150
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DOI: https://doi.org/10.1007/JHEP09(2023)150