### 2D Kac-Moody symmetry of 4D Yang-Mills theory

Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.

- Publication Date:

- Grant/Contract Number:
- FG02-91ER40654

- Type:
- Accepted Manuscript

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

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2016; Journal Issue: 10; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Research Org:
- President & Fellows of Harvard College, Cambridge, MA (United States)

- Sponsoring Org:
- USDOE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Gauge Symmetry; Scattering Amplitudes; Spontaneous Symmetry Breaking

- OSTI Identifier:
- 1362020

```
He, Temple, Mitra, Prahar, and Strominger, Andrew.
```*2D Kac-Moody symmetry of 4D Yang-Mills theory*. United States: N. p.,
Web. doi:10.1007/JHEP10(2016)137.

```
He, Temple, Mitra, Prahar, & Strominger, Andrew.
```*2D Kac-Moody symmetry of 4D Yang-Mills theory*. United States. doi:10.1007/JHEP10(2016)137.

```
He, Temple, Mitra, Prahar, and Strominger, Andrew. 2016.
"2D Kac-Moody symmetry of 4D Yang-Mills theory". United States.
doi:10.1007/JHEP10(2016)137. https://www.osti.gov/servlets/purl/1362020.
```

```
@article{osti_1362020,
```

title = {2D Kac-Moody symmetry of 4D Yang-Mills theory},

author = {He, Temple and Mitra, Prahar and Strominger, Andrew},

abstractNote = {Scattering amplitudes of any four-dimensional theory with nonabelian gauge group G may be recast as two-dimensional correlation functions on the asymptotic twosphere at null in nity. The soft gluon theorem is shown, for massless theories at the semiclassical level, to be the Ward identity of a holomorphic two-dimensional G-Kac-Moody symmetry acting on these correlation functions. Holomorphic Kac-Moody current insertions are positive helicity soft gluon insertions. Furthermore, the Kac-Moody transformations are a CPT invariant subgroup of gauge transformations which act nontrivially at null in nity and comprise the four-dimensional asymptotic symmetry group.},

doi = {10.1007/JHEP10(2016)137},

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

number = 10,

volume = 2016,

place = {United States},

year = {2016},

month = {10}

}