## Toda theory from six dimensions

## Abstract

We describe a compactification of the six-dimensional (2,0) theory on a foursphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and twodimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.

- Authors:

- Inst. for Advanced Study, Princeton, NJ (United States). School for National Sciences
- Harvard Univ., Cambridge, MA (United States). Jefferson Physical Lab.

- Publication Date:

- Research Org.:
- Inst. for Advanced Study, Princeton, NJ (United States)

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

- OSTI Identifier:
- 1502497

- Grant/Contract Number:
- SC0009988

- 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: 2017; Journal Issue: 12; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Effective Field Theories; Field Theories in Higher Dimensions; Supersymmetric Gauge Theory; Topological Field Theories

### Citation Formats

```
Córdova, Clay, and Jafferis, Daniel L. Toda theory from six dimensions. United States: N. p., 2017.
Web. doi:10.1007/jhep12(2017)106.
```

```
Córdova, Clay, & Jafferis, Daniel L. Toda theory from six dimensions. United States. doi:10.1007/jhep12(2017)106.
```

```
Córdova, Clay, and Jafferis, Daniel L. Tue .
"Toda theory from six dimensions". United States. doi:10.1007/jhep12(2017)106. https://www.osti.gov/servlets/purl/1502497.
```

```
@article{osti_1502497,
```

title = {Toda theory from six dimensions},

author = {Córdova, Clay and Jafferis, Daniel L.},

abstractNote = {We describe a compactification of the six-dimensional (2,0) theory on a foursphere which gives rise to a two-dimensional Toda theory at long distances. This construction realizes chiral Toda fields as edge modes trapped near the poles of the sphere. We relate our setup to compactifications of the (2,0) theory on the five and six-sphere. In this way, we explain a connection between half-BPS operators of the (2,0) theory and twodimensional W-algebras, and derive an equality between their conformal anomalies. As we explain, all such relationships between the six-dimensional (2,0) theory and Toda field theory can be interpreted as statements about the edge modes of complex Chern-Simons on various three-manifolds with boundary.},

doi = {10.1007/jhep12(2017)106},

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

number = 12,

volume = 2017,

place = {United States},

year = {2017},

month = {12}

}

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Cited by: 5 works

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