### Abstract

We present a general discussion on the possible existence of an Atkin-Lehner symmetry leading to a zero cosmological constant in lattice compactified heterotic string theories. We explicitly find such a symmetry to be impossible for four dimensional strings (with the simplest world-sheet supersymmetry) by enumerating all the possible partition functions. We also show, in more generality, that an Atkin-Lehner symmetry is incompatible with general physical constraints on the singularity structure of the string amplitude in moduli space expect for a unique partition function (related to the Leech lattice) in two space-time dimensions. Therefore those theories with space-time supersymmetry remain the only known examples with vanishing cosmological constant in greater than two space-time dimensions.

Original language | English |
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Pages (from-to) | 387-414 |

Number of pages | 28 |

Journal | Nuclear Physics, Section B |

Volume | 319 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 12 1989 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

*Nuclear Physics, Section B*,

*319*(2), 387-414. https://doi.org/10.1016/0550-3213(89)90083-7