Extended supersymmetric sigma models in AdS_{4} from projective superspace
Abstract
There exist two superspace approaches to describe {N} = 2 supersymmetric nonlinear σmodels in fourdimensional antide Sitter (AdS_{4}) space: (i) in terms of {N} = 1 AdS chiral superfields, as developed in arXiv:1105.3111 and arXiv:1108.5290; and (ii) in terms of {N} = 2 polar supermultiplets using the AdS projectivesuperspace techniques developed in arXiv:0807.3368. The virtue of the approach (i) is that it makes manifest the geometric properties of the {N} = 2 supersymmetric σmodels in AdS_{4}. The target space must be a noncompact hyperkähler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the twosphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkähler metrics as well as to address the problem of deformations of such metrics. Here we show how to relate the formulation (ii) to (i) by integrating out an infinite number of {N} = 1 AdS auxiliary superfields and performing a superfield duality transformation. We also develop a novel description of the most general {N} = 2 supersymmetric nonlinear σmodel in AdS_{4} in terms of chiral superfields on threedimensional {N} = 2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the fourdimensional {N} = 2 AdS superspace that makes use of Poincaré coordinates for AdS_{4}. This novel formulation allows us to uncover several interesting geometric results.
 Publication:

Journal of High Energy Physics
 Pub Date:
 May 2012
 DOI:
 10.1007/JHEP05(2012)138
 arXiv:
 arXiv:1203.5001
 Bibcode:
 2012JHEP...05..138B
 Keywords:

 Supersymmetry and Duality;
 Extended Supersymmetry;
 Superspaces;
 Supersymmetric Effective Theories;
 High Energy Physics  Theory
 EPrint:
 88 pages