# Cluster adjacency for *m* = 2 Yangian invariants

## Abstract

We classify the rational Yangian invariants of the m = 2 toy model of N = 4 Yang-Mills theory in terms of generalised triangles inside the amplituhedron $A$$^{(2)}_{n,k}$$. We enumerate and provide an explicit formula for all invariants for any number of particles n and any helicity degree k. Each invariant manifestly satisfies cluster adjacency with respect to the Gr(2, n) cluster algebra.

- Authors:

- Univ. of Hertfordshire (United Kingdom)
- Univ. of Oxford (United Kingdom)
- Brown Univ., Providence, RI (United States)

- Publication Date:

- Research Org.:
- Brown Univ., Providence, RI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Simons Foundation; National Science Foundation (NSF); CERN Theory Group

- OSTI Identifier:
- 1594823

- Grant/Contract Number:
- SC0010010; 376208; PHY-1607611

- 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: 2019; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Supersymmetric Gauge Theory

### Citation Formats

```
Łukowski, Tomasz, Parisi, Matteo, Spradlin, Marcus, and Volovich, Anastasia. Cluster adjacency for m = 2 Yangian invariants. United States: N. p., 2019.
Web. doi:10.1007/JHEP10(2019)158.
```

```
Łukowski, Tomasz, Parisi, Matteo, Spradlin, Marcus, & Volovich, Anastasia. Cluster adjacency for m = 2 Yangian invariants. United States. doi:10.1007/JHEP10(2019)158.
```

```
Łukowski, Tomasz, Parisi, Matteo, Spradlin, Marcus, and Volovich, Anastasia. Mon .
"Cluster adjacency for m = 2 Yangian invariants". United States. doi:10.1007/JHEP10(2019)158. https://www.osti.gov/servlets/purl/1594823.
```

```
@article{osti_1594823,
```

title = {Cluster adjacency for m = 2 Yangian invariants},

author = {Łukowski, Tomasz and Parisi, Matteo and Spradlin, Marcus and Volovich, Anastasia},

abstractNote = {We classify the rational Yangian invariants of the m = 2 toy model of N = 4 Yang-Mills theory in terms of generalised triangles inside the amplituhedron $A$$^{(2)}_{n,k}$. We enumerate and provide an explicit formula for all invariants for any number of particles n and any helicity degree k. Each invariant manifestly satisfies cluster adjacency with respect to the Gr(2, n) cluster algebra.},

doi = {10.1007/JHEP10(2019)158},

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

number = 10,

volume = 2019,

place = {United States},

year = {2019},

month = {10}

}

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