Extended supersymmetric sigma models in AdS_4 from projective superspace

摘要

There exist two superspace approaches to describe N=2 supersymmetricnonlinear sigma models in four-dimensional anti-de Sitter (AdS_4) space: (i) interms of N=1 AdS chiral superfields, as developed in arXiv:1105.3111 andarXiv:1108.5290; and (ii) in terms of N=2 polar supermultiplets using the AdSprojective-superspace techniques developed in arXiv:0807.3368. The virtue ofthe approach (i) is that it makes manifest the geometric properties of the N=2supersymmetric sigma-models in AdS_4. The target space must be a non-compacthyperkahler manifold endowed with a Killing vector field which generates anSO(2) group of rotations on the two-sphere of complex structures. The power ofthe approach (ii) is that it allows us, in principle, to generate hyperkahlermetrics 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 aninfinite number of N=1 AdS auxiliary superfields and performing a superfieldduality transformation. We also develop a novel description of the most generalN=2 supersymmetric nonlinear sigma-model in AdS_4 in terms of chiralsuperfields on three-dimensional N=2 flat superspace without central charge.This superspace naturally originates from a conformally flat realization forthe four-dimensional N=2 AdS superspace that makes use of Poincare coordinatesfor AdS_4. This novel formulation allows us to uncover several interestinggeometric results.