### Cluster functions and scattering amplitudes for six and seven points

Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. Here, we explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.

- Publication Date:

- Grant/Contract Number:
- SC0010010

- Type:
- 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: 7; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

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

- Sponsoring Org:
- USDOE Office of Science (SC)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; scattering amplitudes; supersymmetries gauge theory

- OSTI Identifier:
- 1393149

```
Harrington, Thomas, and Spradlin, Marcus.
```*Cluster functions and scattering amplitudes for six and seven points*. United States: N. p.,
Web. doi:10.1007/JHEP07(2017)016.

```
Harrington, Thomas, & Spradlin, Marcus.
```*Cluster functions and scattering amplitudes for six and seven points*. United States. doi:10.1007/JHEP07(2017)016.

```
Harrington, Thomas, and Spradlin, Marcus. 2017.
"Cluster functions and scattering amplitudes for six and seven points". United States.
doi:10.1007/JHEP07(2017)016. https://www.osti.gov/servlets/purl/1393149.
```

```
@article{osti_1393149,
```

title = {Cluster functions and scattering amplitudes for six and seven points},

author = {Harrington, Thomas and Spradlin, Marcus},

abstractNote = {Scattering amplitudes in planar super-Yang-Mills theory satisfy several basic physical and mathematical constraints, including physical constraints on their branch cut structure and various empirically discovered connections to the mathematics of cluster algebras. The power of the bootstrap program for amplitudes is inversely proportional to the size of the intersection between these physical and mathematical constraints: ideally we would like a list of constraints which determine scattering amplitudes uniquely. Here, we explore this intersection quantitatively for two-loop six- and seven-point amplitudes by providing a complete taxonomy of the Gr(4, 6) and Gr(4, 7) cluster polylogarithm functions of [15] at weight 4.},

doi = {10.1007/JHEP07(2017)016},

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

number = 7,

volume = 2017,

place = {United States},

year = {2017},

month = {7}

}