### Abstract

We generalize the standard N=2 supersymmetric Kazama-Suzuki coset construction to the N=4 case by requiring the nonlinear (Goddard-Schwimmer) N=4 quasisuperconformal algebra to be realized on cosets. The constraints that we find allow a very simple geometrical interpretation and have the Wolf spaces as their natural solutions. Our results obtained by using component-level superconformal field theory methods are fully consistent with standard results about N=4 supersymmetric two-dimensional nonlinear σ models and N=4 WZWN models on Wolf spaces. We construct the actions for the latter and express the quaternionic structure, appearing in the N=4 coset solution, in terms of the symplectic structure associated with the underlying Freudenthal triple system. Next, we gauge the N=4 QSCA and build a quantum BRST charge for the N=4 string propagating on a Wolf space. Surprisingly, the BRST charge nilpotency conditions rule out the nontrivial Wolf spaces as consistent string backgrounds.

Original language | English |
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Pages (from-to) | 2278-2293 |

Number of pages | 16 |

Journal | Physical Review D |

Volume | 52 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D*,

*52*(4), 2278-2293. https://doi.org/10.1103/PhysRevD.52.2278