### Abstract

We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2)Kač-Moody subalgebras. For the range 3 ≤ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h, and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.

Original language | English (US) |
---|---|

Pages (from-to) | 402-430 |

Number of pages | 29 |

Journal | Nuclear Physics, Section B |

Volume | 322 |

Issue number | 2 |

DOIs | |

State | Published - Aug 14 1989 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*322*(2), 402-430. https://doi.org/10.1016/0550-3213(89)90421-5

}

*Nuclear Physics, Section B*, vol. 322, no. 2, pp. 402-430. https://doi.org/10.1016/0550-3213(89)90421-5

**On the unitary representations of a class of N = 4 superconformal algebras.** / Gunaydin, Murat; Petersen, J. L.; Taormina, A.; Van Proeyen, A.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the unitary representations of a class of N = 4 superconformal algebras

AU - Gunaydin, Murat

AU - Petersen, J. L.

AU - Taormina, A.

AU - Van Proeyen, A.

PY - 1989/8/14

Y1 - 1989/8/14

N2 - We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2)Kač-Moody subalgebras. For the range 3 ≤ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h, and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.

AB - We derive properties of unitary highest weight representations of the N = 4 superconformal algebras in 2 dimensions, characterized by two SU(2)Kač-Moody subalgebras. For the range 3 ≤ c < 6 we can prove that we have constructed all unitary highest weight representations. These reduce in N = 2 to the discrete series. For other values of the parameters we derive bounds on the values of h, and we conjecture that these are complete. This is motivated by explicit constructions of representations for various values of the parameters. For the so-called massless representations we do indeed prove that our treatment is complete.

UR - http://www.scopus.com/inward/record.url?scp=0000195004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000195004&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(89)90421-5

DO - 10.1016/0550-3213(89)90421-5

M3 - Article

AN - SCOPUS:0000195004

VL - 322

SP - 402

EP - 430

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2

ER -