### 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 |

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### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Four-loop divergences of the two-dimensional (1,1) supersymmetric non-linear sigma model with a Wess-Zumino-Witten term.** / Deriglazov, A. A.; Ketov, S. V.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 359, no. 2-3, pp. 498-544. https://doi.org/10.1016/0550-3213(91)90070-E

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TY - JOUR

T1 - Four-loop divergences of the two-dimensional (1,1) supersymmetric non-linear sigma model with a Wess-Zumino-Witten term

AU - Deriglazov, A. A.

AU - Ketov, S. V.

PY - 1991/8/5

Y1 - 1991/8/5

N2 - 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.

AB - 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.

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U2 - 10.1016/0550-3213(91)90070-E

DO - 10.1016/0550-3213(91)90070-E

M3 - Article

VL - 359

SP - 498

EP - 544

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 2-3

ER -