Extended supersymmetric sigma models in AdS_4 from projective superspace

TL;DR

This paper explores two superspace methods for describing N=2 supersymmetric sigma models in AdS_4, relating them through superfield duality and introducing a new 3D N=2 flat superspace formulation to analyze geometric properties.

Contribution

It establishes a connection between two superspace approaches and introduces a novel 3D N=2 superspace formulation for AdS_4 sigma models.

Findings

Relation between two superspace formulations via superfield duality.

New 3D N=2 flat superspace description of sigma models.

Geometric insights into hyperkahler target spaces in AdS_4.

Abstract

There exist two superspace approaches to describe N=2 supersymmetric nonlinear sigma models in four-dimensional anti-de 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 projective-superspace 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 sigma-models in AdS_4. The target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures. The power of the approach (ii) is that it allows us, in principle, to generate hyperkahler 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 sigma-model in AdS_4 in terms of chiral superfields on three-dimensional N=2 flat superspace without central charge. This superspace naturally originates from a conformally flat realization for the four-dimensional N=2 AdS superspace that makes use of Poincare coordinates for AdS_4. This novel formulation allows us to uncover several interesting geometric results.