Abstract
Coulomb branch chiral rings of \( \mathcal{N}=2 \) SCFTs are conjectured to be freely generated. While no counter-example is known, no direct evidence for the conjecture is known either. We initiate a systematic study of SCFTs with Coulomb branch chiral rings satisfying non-trivial relations, restricting our analysis to rank 1. The main result of our study is that (rank-1) SCFTs with non-freely generated CB chiral rings when deformed by relevant deformations, always flow to theories with non-freely generated CB rings. This implies that if they exist, they must thus form a distinct subset under RG flows. We also find many interesting characteristic properties that these putative theories satisfy which may behelpful in proving or disproving their existence using other methods.
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Argyres, P.C., Lü, Y. & Martone, M. Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated. J. High Energ. Phys. 2017, 144 (2017). https://doi.org/10.1007/JHEP06(2017)144
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DOI: https://doi.org/10.1007/JHEP06(2017)144