Abstract
We propose a unified perspective on two sets of objects that usually arise in the study of bipartite field theories. Each of the sets consists of a polytope, or equivalently a toric Calabi-Yau, and a quiver theory. We refer to the two sets of objects as original and twin. In the simplest cases, the two sides of the correspondence are connected by the graph operation known as untwisting. The democratic treatment that we advocate raises new questions regarding the connections between these objects, some of which we explore.
With this motivation in mind, we establish a correspondence between the mutations of the original polytope and the twin quiver. This leads us to propose that non-toric twin quivers are naturally associated to generalized toric polygons (GTPs) and we explore various aspects of this idea. Supporting evidence includes global symmetries, the ability of twin quivers to encode the generalized s-rule, and the connection between the mutations of polytopes and of configurations of webs of 5-branes suspended from 7-branes. We introduce three methods for constructing twin quivers for GTPs. We also investigate the connection between twin quivers obtained using different toric phases. Twin quivers provide a powerful new perspective on GTPs. The ideas presented in this paper may represent a step towards the generalization of brane tilings to GTPs.
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Acknowledgments
S.F. would like to thank Diego Rodríguez-Gómez for stimulating discussions and encouragement. S.F was supported by the U.S. National Science Foundation grants PHY-2112729 and DMS-1854179. 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 a UNIST Fundamental Science Research Grant (1.220123.01), 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).
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Franco, S., Seong, RK. Twin theories, polytope mutations and quivers for GTPs. J. High Energ. Phys. 2023, 34 (2023). https://doi.org/10.1007/JHEP07(2023)034
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DOI: https://doi.org/10.1007/JHEP07(2023)034