Three-dimensional (p,q) AdS superspaces and matter couplings
Abstract
We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q<=4 (for N>4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.
Keywords
Cite
@article{arxiv.1205.4622,
title = {Three-dimensional (p,q) AdS superspaces and matter couplings},
author = {Sergei M. Kuzenko and Ulf Lindstrom and Gabriele Tartaglino-Mazzucchelli},
journal= {arXiv preprint arXiv:1205.4622},
year = {2012}
}
Comments
52 pages; V3: minor corrections, version published in JHEP