### 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 |
---|---|

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

**No N=4 strings on Wolf spaces.** / Gates, S. James; Ketov, Sergei V.

Research output: Contribution to journal › Article

*Physical Review D*, vol. 52, no. 4, pp. 2278-2293. https://doi.org/10.1103/PhysRevD.52.2278

}

TY - JOUR

T1 - No N=4 strings on Wolf spaces

AU - Gates, S. James

AU - Ketov, Sergei V.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001147105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001147105&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.52.2278

DO - 10.1103/PhysRevD.52.2278

M3 - Article

VL - 52

SP - 2278

EP - 2293

JO - Physical review D: Particles and fields

JF - Physical review D: Particles and fields

SN - 1550-7998

IS - 4

ER -