# $$ \mathcal{N}=1 $$ deformations and RG flows of $$ \mathcal{N}=2 $$ SCFTs

## Abstract

Here, we study certain $$ \mathcal{N}=1 $$ preserving deformations of four-dimensional $$ \mathcal{N}=2 $$ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $$ \mathcal{N}=1 $$ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $$ \mathcal{N}=2 $$ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the ( *A _{1},A_{n}*) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the (

*A*) theories and find agreements with the previous results. Furthermore, we study the cases, including the

_{1},A_{n}*T*and

_{N}*R*theories of class S and some of rank-one SCFTs, where the deformation gives genuine $$ \mathcal{N}=1 $$ fixed points.

_{0,N}- Authors:

- Imperial College, London (United Kingdom); Seikei Univ., Tokyo (Japan)
- Univ. of California, San Diego, La Jolla, CA (United States)

- Publication Date:

- Research Org.:
- Univ. of California, San Diego, CA (United States); Imperial College London, London (United Kingdom)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1356082

- Alternate Identifier(s):
- OSTI ID: 1358375

- Grant/Contract Number:
- SC0009919

- Resource Type:
- Journal Article: Accepted Manuscript

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

- Additional Journal Information:
- Journal Volume: 2017; Journal Issue: 2; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; supersymmetric gauge theory; F-theory; global symmetry; duality; QCD; conformal field theory; renormalization group; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Maruyoshi, Kazunobu, and Song, Jaewon.
```*$ \mathcal{N}=1 $ deformations and RG flows of $ \mathcal{N}=2 $ SCFTs*. United States: N. p., 2017.
Web. doi:10.1007/JHEP02(2017)075.

```
Maruyoshi, Kazunobu, & Song, Jaewon.
```*$ \mathcal{N}=1 $ deformations and RG flows of $ \mathcal{N}=2 $ SCFTs*. United States. doi:10.1007/JHEP02(2017)075.

```
Maruyoshi, Kazunobu, and Song, Jaewon. Tue .
"$ \mathcal{N}=1 $ deformations and RG flows of $ \mathcal{N}=2 $ SCFTs". United States. doi:10.1007/JHEP02(2017)075. https://www.osti.gov/servlets/purl/1356082.
```

```
@article{osti_1356082,
```

title = {$ \mathcal{N}=1 $ deformations and RG flows of $ \mathcal{N}=2 $ SCFTs},

author = {Maruyoshi, Kazunobu and Song, Jaewon},

abstractNote = {Here, we study certain $ \mathcal{N}=1 $ preserving deformations of four-dimensional $ \mathcal{N}=2 $ superconformal field theories (SCFTs) with non-abelian flavor symmetry. The deformation is described by adding an $ \mathcal{N}=1 $ chiral multiplet transforming in the adjoint representation of the flavor symmetry with a superpotential coupling, and giving a nilpotent vacuum expectation value to the chiral multiplet which breaks the flavor symmetry. This triggers a renormalization group flow to an infrared SCFT. Remarkably, we find classes of theories flow to enhanced $ \mathcal{N}=2 $ supersymmetric fixed points in the infrared under the deformation. They include generalized Argyres-Douglas theories and rank-one SCFTs with non-abelian flavor symmetries. Most notably, we find renormalization group flows from the deformed conformal SQCDs to the (A1,An) Argyres-Douglas theories. From these "Lagrangian descriptions," we compute the full superconformal indices of the (A1,An) theories and find agreements with the previous results. Furthermore, we study the cases, including the TN and R0,N theories of class S and some of rank-one SCFTs, where the deformation gives genuine $ \mathcal{N}=1 $ fixed points.},

doi = {10.1007/JHEP02(2017)075},

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

issn = {1029-8479},

number = 2,

volume = 2017,

place = {United States},

year = {2017},

month = {2}

}

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