# Infinitely many $$ \mathcal{N}=1 $$ dualities from m + 1 - m = 1

## Abstract

We discuss two infinite classes of 4d supersymmetric theories, T _{N} ^{(m)} and U$$(m)\atop{N}$$, labelled by an arbitrary non-negative integer, m. The T _{N} ^{(m)} theory arises from the 6d, A _{N-1} type N=(2,0) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m + 1, -m); the m = 0 case is the N=2 supersymmetric T _{N} theory. The novelty is the negative-degree line bundle. The U$$(m)\atop{N}$$ theories likewise arise from the 6d N=(2,0) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) T _{N} ^{(m)} theories. The T _{N} ^{(m)} and U$$(m)\atop{N}$$ theories can be represented, in various duality frames, as quiver gauge theories, built from T _{N} components via gauging and nilpotent Higgsing. We analyze the RG flow of the U($$(m)\atop{N}$$ theories, and find that, for all integer m > 0, they end up at the same IR SCFT as SU(N) SQCD with 2N flavors and quartic superpotential. The U$$(m)\atop{N}$$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with N _{f} = 2N _{c}. The U$$(m)\atop{N}$$ duals have different duality frame quiver representations, with 2m + 1 gauge nodes.

- Authors:

- University of California, San Diego, La Jolla, CA (United States). Department of Physics

- Publication Date:

- Research Org.:
- University of California, San Diego, La Jolla, CA (United States). Department of Physics

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1434593

- Grant/Contract Number:
- SC0009919

- Resource Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Super symmetric gauge theory; Brane Dynamics in Gauge Theories; Duality in Gauge Field Theories; Renormalization Group

### Citation Formats

```
Agarwal, Prarit, Intriligator, Kenneth, and Song, Jaewon. Infinitely many $ \mathcal{N}=1 $ dualities from m + 1 - m = 1. United States: N. p., 2015.
Web. doi:10.1007/JHEP10(2015)035.
```

```
Agarwal, Prarit, Intriligator, Kenneth, & Song, Jaewon. Infinitely many $ \mathcal{N}=1 $ dualities from m + 1 - m = 1. United States. doi:10.1007/JHEP10(2015)035.
```

```
Agarwal, Prarit, Intriligator, Kenneth, and Song, Jaewon. Tue .
"Infinitely many $ \mathcal{N}=1 $ dualities from m + 1 - m = 1". United States. doi:10.1007/JHEP10(2015)035. https://www.osti.gov/servlets/purl/1434593.
```

```
@article{osti_1434593,
```

title = {Infinitely many $ \mathcal{N}=1 $ dualities from m + 1 - m = 1},

author = {Agarwal, Prarit and Intriligator, Kenneth and Song, Jaewon},

abstractNote = {We discuss two infinite classes of 4d supersymmetric theories, TN(m) and U$(m)\atop{N}$, labelled by an arbitrary non-negative integer, m. The TN(m) theory arises from the 6d, AN-1 type N=(2,0) theory reduced on a 3-punctured sphere, with normal bundle given by line bundles of degree (m + 1, -m); the m = 0 case is the N=2 supersymmetric TN theory. The novelty is the negative-degree line bundle. The U$(m)\atop{N}$ theories likewise arise from the 6d N=(2,0) theory on a 4-punctured sphere, and can be regarded as gluing together two (partially Higgsed) TN(m) theories. The TN(m) and U$(m)\atop{N}$ theories can be represented, in various duality frames, as quiver gauge theories, built from TN components via gauging and nilpotent Higgsing. We analyze the RG flow of the U($(m)\atop{N}$ theories, and find that, for all integer m > 0, they end up at the same IR SCFT as SU(N) SQCD with 2N flavors and quartic superpotential. The U$(m)\atop{N}$ theories can thus be regarded as an infinite set of UV completions, dual to SQCD with Nf = 2N c. The U$(m)\atop{N}$ duals have different duality frame quiver representations, with 2m + 1 gauge nodes.},

doi = {10.1007/JHEP10(2015)035},

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

number = 10,

volume = 2015,

place = {United States},

year = {2015},

month = {10}

}

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