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

## Abstract

Coulomb branch chiral rings of 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 nd many interesting characteristic properties that these putative theories satisfy which may be helpful in proving or disproving their existence using other methods.

- Authors:

- Univ. of Cincinnati, OH (United States)

- Publication Date:

- Research Org.:
- Univ. of Cincinnati, OH (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1424739

- Grant/Contract Number:
- SC0011784

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 6; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal and W Symmetry; Conformal Field Theory; Extended Super-symmetry

### Citation Formats

```
Argyres, Philip C., Lü, Yongchao, and Martone, Mario.
```*Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated*. United States: N. p., 2017.
Web. doi:10.1007/JHEP06(2017)144.

```
Argyres, Philip C., Lü, Yongchao, & Martone, Mario.
```*Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated*. United States. doi:10.1007/JHEP06(2017)144.

```
Argyres, Philip C., Lü, Yongchao, and Martone, Mario. Tue .
"Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated". United States.
doi:10.1007/JHEP06(2017)144. https://www.osti.gov/servlets/purl/1424739.
```

```
@article{osti_1424739,
```

title = {Seiberg-Witten geometries for Coulomb branch chiral rings which are not freely generated},

author = {Argyres, Philip C. and Lü, Yongchao and Martone, Mario},

abstractNote = {Coulomb branch chiral rings of 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 nd many interesting characteristic properties that these putative theories satisfy which may be helpful in proving or disproving their existence using other methods.},

doi = {10.1007/JHEP06(2017)144},

journal = {Journal of High Energy Physics (Online)},

number = 6,

volume = 2017,

place = {United States},

year = {Tue Jun 27 00:00:00 EDT 2017},

month = {Tue Jun 27 00:00:00 EDT 2017}

}

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