Lectures on nonlinear sigma-models in projective superspace
Abstract
N = 2 supersymmetry in four space-time dimensions is intimately related to hyperkahler and quaternionic Kahler geometries. On one hand, the target spaces for rigid supersymmetric sigma-models are necessarily hyperkahler manifolds. On the other hand, when coupled to N = 2 supergravity, the sigma-model target spaces must be quaternionic Kahler. It is known that such manifolds of restricted holonomy are difficult to generate explicitly. Projective superspace is a field-theoretic approach to constructing general N = 2 supersymmetric nonlinear sigma-models, and hence to generate new hyperkahler and quaternionic Kahler metrics. Intended for a mixed audience consisting of both physicists and mathematicians, these lectures provide a pedagogical introduction to the projective-superspace approach.
Cite
@article{arxiv.1004.0880,
title = {Lectures on nonlinear sigma-models in projective superspace},
author = {Sergei M. Kuzenko},
journal= {arXiv preprint arXiv:1004.0880},
year = {2012}
}
Comments
56 pages. Lectures given at the 30th Winter School Geometry and Physics, Srni, Czech Republic, 16--23 January, 2010. V2: typos corrected, comments added; V3: almost published version (quotation from Osip Mandelstam was removed by J. Phys. A from published article)