### Abstract

The four-loop divergences of the (1,1) supersymmetric two-dimensional non-linear σ-model with a Wess-Zumino-Witten term are analyzed. All the four-loop 1/ε{lunate}-divergences in the general case (and an overall coefficient at the total four-loop contribution to the β-function) are shown to be reducible to only structures proportional to ξ(3). We explicitly calculate non-derivative contributions to the four-loop β-function from logarithmically divergent graphs. As a by-product, we obtain the complete four-loop β-function for the supersymmetric Wess-Zumino-Witten model. We use the partial results for the general four-loop β-function to shed some light on the structure of the (α′)^{3}-corrections to the superstring effective-action with antisymmetric-tensor field coupling. An inconsistency of the supersymmetrical dimensional regularisation via dimensional reduction in the presence of torsion is discovered at four loops, unless the string interpretation for the σ-model is adopted.

Original language | English |
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Pages (from-to) | 498-544 |

Number of pages | 47 |

Journal | Nuclear Physics, Section B |

Volume | 359 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 5 Aug 1991 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics