Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated

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.

40 pages, 4 tables

References in corpus (2)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Mass deformations of four-dimensional, rank 1, N=2 superconformal field theories

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