Lectures on nonlinear sigma-models in projective superspace

Details Lectures on nonlinear sigma-models in projective superspace Lectures on nonlinear sigma-models in projective superspace

2010-04-06

arxiv.org/abs/1004.0880v3

J.Phys.A43:443001,2010

Physics

High Energy Physics

High Energy Physics - Theory

56 pages. Lectures given at the 30th Winter School Geometry and Physics, Srni, Czech Republic, 16--23 January, 2010. V2: typos

Scientific paper

10.1088/1751-8113/43/44/443001

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.

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