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

A. A. Deriglazov, S. V. Ketov

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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 languageEnglish
Pages (from-to)498-544
Number of pages47
JournalNuclear Physics, Section B
Issue number2-3
Publication statusPublished - 5 Aug 1991


ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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