Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

Luis Alvarez-Gaume; Daniel Z. Freedman

doi:10.1007/BF01208280

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

Luis Alvarez-Gaume
, Daniel Z. Freedman

Simons Center for Geometry & Physics

Stony Brook University

Massachusetts Institute of Technology
Stony Brook University

Research output: Contribution to journal › Article › peer-review

505 Scopus citations

Abstract

A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory.

Original language	English
Pages (from-to)	443-451
Number of pages	9
Journal	Communications in Mathematical Physics
Volume	80
Issue number	3
DOIs	https://doi.org/10.1007/BF01208280
State	Published - Sep 1981

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title = "Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model",

abstract = "A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory.",

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AB - A complete geometrical classification of supersymmetric σ-models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory.

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JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

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Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

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