supersymmetric sigma model geometry超对称模型几何.pdfVIP

Symmetry 2012, 4, 474-506; doi:10.3390/sym4030474 OPEN ACCESS symmetry ISSN 2073-8994 /journal/symmetry Article Supersymmetric Sigma Model Geometry ¨ Ulf Lindstrom Theoretical Physics, Department of Physics and Astronomy, Uppsala University, Box 516, Uppsala 75120, Sweden; E-Mail: ulf.lindstrom@physics.uu.se; Tel.: +46-18-471-3298; Fax: +46-18-533-180 Received: 6 July 2012; in revised form: 23 July 2012 / Accepted: 2 August 2012 / Published: 23 August 2012 Abstract: This is a review of how sigma models formulated in Superspace have become ¨ important tools for understanding geometry. Topics included are: The (hyper)kahler ¨ reduction; projective superspace; the generalized Legendre construction; generalized Kahler ¨ geometry and constructions of hyperkahler metrics on Hermitian symmetric spaces. Keywords: supersymmetry; complex geometry; sigma models Classification: PACS 11.30.Pb Classification: MSC 53Z05 1. Introduction Sigma models take their name from a phenomenological model of beta decay introduced more than ´ fifty years ago by Gell-Mann and Levy [ 1]. It contains pions and a new scalar meson that they called sigma. A generalization of this model is what is nowadays meant by a si