Lectures on nonlinear sigma-models in projective superspace

Sergei M Kuzenko

    Research output: Contribution to journal › Review article

    37 Citations (Scopus)

    Abstract

    N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkähler and quaternionic Kähler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkähler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kähler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkähler and quaternionic Kähler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.

    Original languageEnglish
    Article number443001
    JournalJournal of Physics A: Mathematical and Theoretical
    Volume43
    DOIs
    Publication statusPublished - 2010

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    Nonlinear sigma Model
    Superspaces
    Sigma Models
    lectures
    Target
    Holonomy
    Supergravity
    Supersymmetry
    Space-time
    supergravity
    Metric
    supersymmetry
    Geometry
    geometry

    Cite this

    Kuzenko, Sergei M. / Lectures on nonlinear sigma-models in projective superspace. In: Journal of Physics A: Mathematical and Theoretical. 2010 ; Vol. 43.
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    abstract = "N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperk{\"a}hler and quaternionic K{\"a}hler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperk{\"a}hler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic K{\"a}hler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperk{\"a}hler and quaternionic K{\"a}hler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.",
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    Kuzenko, SM 2010, 'Lectures on nonlinear sigma-models in projective superspace' Journal of Physics A: Mathematical and Theoretical, vol. 43, 443001. https://doi.org/10.1088/1751-8113/43/44/443001

    Lectures on nonlinear sigma-models in projective superspace. / Kuzenko, Sergei M.

    In: Journal of Physics A: Mathematical and Theoretical, Vol. 43, 443001, 2010.

    Research output: Contribution to journal › Review article

    TY - JOUR

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    AU - Kuzenko, Sergei M

    PY - 2010

    Y1 - 2010

    N2 - N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkähler and quaternionic Kähler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkähler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kähler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkähler and quaternionic Kähler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.

    AB - N= 2 supersymmetry in four spacetime dimensions is intimately related to hyperkähler and quaternionic Kähler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkähler manifolds. On the other hand, when coupled to N= 2 supergravity, the sigma-model target spaces must be quaternionic Kähler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to construct general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkähler and quaternionic Kähler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.

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    DO - 10.1088/1751-8113/43/44/443001

    M3 - Review article

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    JO - Journal of Physics A : Mathematical and Theoretical

    JF - Journal of Physics A : Mathematical and Theoretical

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    Kuzenko SM. Lectures on nonlinear sigma-models in projective superspace. Journal of Physics A: Mathematical and Theoretical. 2010;43. 443001. https://doi.org/10.1088/1751-8113/43/44/443001

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