# Higher melonic theories

## Abstract

We classify a large set of melonic theories with arbitrary q-fold interactions, demonstrating that the interaction vertices exhibit a range of symmetries, always of the form Z _{2} ^{n} for some n, which may be 0. The number of different theories proliferates quickly as q increases above 8 and is related to the problem of counting one-factorizations of complete graphs. The symmetries of the interaction vertex lead to an effective interaction strength that enters into the Schwinger-Dyson equation for the two-point function as well as the kernel used for constructing higher-point functions.

- Authors:

- Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1507577

- Grant/Contract Number:
- [FG02-91ER40671; 51116; PHY-1620059]

- 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: 2018; Journal Issue: 9]; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 1/N Expansion; Conformal Field Theory; Nonperturbative Effects

### Citation Formats

```
Gubser, Steven S., Jepsen, Christian, Ji, Ziming, and Trundy, Brian. Higher melonic theories. United States: N. p., 2018.
Web. doi:10.1007/jhep09(2018)049.
```

```
Gubser, Steven S., Jepsen, Christian, Ji, Ziming, & Trundy, Brian. Higher melonic theories. United States. doi:10.1007/jhep09(2018)049.
```

```
Gubser, Steven S., Jepsen, Christian, Ji, Ziming, and Trundy, Brian. Mon .
"Higher melonic theories". United States. doi:10.1007/jhep09(2018)049. https://www.osti.gov/servlets/purl/1507577.
```

```
@article{osti_1507577,
```

title = {Higher melonic theories},

author = {Gubser, Steven S. and Jepsen, Christian and Ji, Ziming and Trundy, Brian},

abstractNote = {We classify a large set of melonic theories with arbitrary q-fold interactions, demonstrating that the interaction vertices exhibit a range of symmetries, always of the form Z2n for some n, which may be 0. The number of different theories proliferates quickly as q increases above 8 and is related to the problem of counting one-factorizations of complete graphs. The symmetries of the interaction vertex lead to an effective interaction strength that enters into the Schwinger-Dyson equation for the two-point function as well as the kernel used for constructing higher-point functions.},

doi = {10.1007/jhep09(2018)049},

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

number = [9],

volume = [2018],

place = {United States},

year = {2018},

month = {9}

}

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