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# A Borcherds–Kac–Moody Superalgebra with Conway Symmetry

## Abstract

We construct here a Borcherds–Kac–Moody (BKM) superalgebra on which the Conway group \(\hbox {Co}_0\) acts faithfully. We show that the BKM algebra is generated by the physical states (BRST cohomology classes) in a chiral superstring theory. Furthermore, we use this construction to produce denominator identities for the chiral partition functions of the Conway module \(V^{s\natural }\), a supersymmetric \(c=12\) chiral conformal field theory whose (twisted) partition functions enjoy moonshine properties and which has automorphism group isomorphic to \(\hbox {Co}_0\). In particular, these functions satisfy a genus zero property analogous to that of monstrous moonshine. Finally, we suggest how one may promote the denominators to spacetime BPS indices in type II string theory, which might thus furnish a physical explanation of the genus zero property of Conway moonshine.

- Authors:

- McGill Univ., Montreal, QC (Canada)
- California Inst. of Technology (CalTech), Pasadena, CA (United States)
- Univ. degli Studi di Padova (Italy); Istituto Nazionale di Fisica Nucleare (INFN), Padua (Italy)

- Publication Date:

- Research Org.:
- California Inst. of Technology (CalTech), Pasadena, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); National Science and Engineering Council of Canada; National Science Foundation (NSF)

- Contributing Org.:
- [Perimeter Institute of Theoretical Physics]

- OSTI Identifier:
- 1597492

- Grant/Contract Number:
- [SC0011632; PHY-1607611]

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Communications in Mathematical Physics

- Additional Journal Information:
- [ Journal Volume: 370; Journal Issue: 2]; Journal ID: ISSN 0010-3616

- Publisher:
- Springer

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING

### Citation Formats

```
Harrison, Sarah M., Paquette, Natalie M., and Volpato, Roberto. A Borcherds–Kac–Moody Superalgebra with Conway Symmetry. United States: N. p., 2019.
Web. doi:10.1007/s00220-019-03518-0.
```

```
Harrison, Sarah M., Paquette, Natalie M., & Volpato, Roberto. A Borcherds–Kac–Moody Superalgebra with Conway Symmetry. United States. doi:10.1007/s00220-019-03518-0.
```

```
Harrison, Sarah M., Paquette, Natalie M., and Volpato, Roberto. Tue .
"A Borcherds–Kac–Moody Superalgebra with Conway Symmetry". United States. doi:10.1007/s00220-019-03518-0.
```

```
@article{osti_1597492,
```

title = {A Borcherds–Kac–Moody Superalgebra with Conway Symmetry},

author = {Harrison, Sarah M. and Paquette, Natalie M. and Volpato, Roberto},

abstractNote = {We construct here a Borcherds–Kac–Moody (BKM) superalgebra on which the Conway group \(\hbox {Co}_0\) acts faithfully. We show that the BKM algebra is generated by the physical states (BRST cohomology classes) in a chiral superstring theory. Furthermore, we use this construction to produce denominator identities for the chiral partition functions of the Conway module \(V^{s\natural }\), a supersymmetric \(c=12\) chiral conformal field theory whose (twisted) partition functions enjoy moonshine properties and which has automorphism group isomorphic to \(\hbox {Co}_0\). In particular, these functions satisfy a genus zero property analogous to that of monstrous moonshine. Finally, we suggest how one may promote the denominators to spacetime BPS indices in type II string theory, which might thus furnish a physical explanation of the genus zero property of Conway moonshine.},

doi = {10.1007/s00220-019-03518-0},

journal = {Communications in Mathematical Physics},

number = [2],

volume = [370],

place = {United States},

year = {2019},

month = {7}

}

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