### Abstract

Original language | English |
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Article number | 443001 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 43 |

DOIs | |

Publication status | Published - 2010 |

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

Research output: Contribution to journal › Review article

TY - JOUR

T1 - Lectures on nonlinear sigma-models in projective superspace

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.

U2 - 10.1088/1751-8113/43/44/443001

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

M3 - Review article

VL - 43

JO - Journal of Physics A : Mathematical and Theoretical

JF - Journal of Physics A : Mathematical and Theoretical

SN - 1751-8113

M1 - 443001

ER -